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Talk:Koch snowflake

So... what's the definition?
There's no formal definition for what the Koch snowflake *is*. I assume that, like most curves, it's defined as a subset of R². Where is the actual definition of that set? I see a definition of a sequence of curves K_1, K_2, K_3, ..., but saying, as the article does, that the Kock snowflake is "the limit" of this sequence doesn't mean anything. Limit in what sense? The set of points x such that any neighborhood of x intersects K_n for all sufficiently large n? Gaiacarra (talk) 23:42, 7 October 2016 (UTC)
 * Yes, this article is severely flawed for not including a formal definition. Other discussion further down this talk page [] may help, but it needs to be actually incorporated into the article. Jess_Riedel (talk) 03:04, 24 January 2021 (UTC)

3d koch snowflake
I notice that there's a mention of a 3d koch snowflake at the bottom of the page, but no link to get a picture. I found a picture here: http://graphics.ucsd.edu/~henrik/images/sflake.jpg but it isn't really a straightforward extension of the planar curve. I'd like to submit the construction on my website at: http://people.reed.edu/~goldena/solid-koch.html for consideration, if we want to have a 3d koch snowflake on this page. I hereby waive my copyright on the images at http://people.reed.edu/~goldena/solid-koch.html. They are in the public domain to be used by anyone for any purpose. 74.93.190.190 02:27, 14 March 2007 (UTC) goldena

This page was vandalised yesterday and i don't know how to change it back

See How_to_revert_a_page_to_an_earlier_version. —Tobias Bergemann 09:13, 19 November 2005 (UTC)

Should we change references here to the "von Koch snowflake"? Dysprosia 00:12, 17 Nov 2003 (UTC)

I certainly wouldn't mind; however, I think (in general) the von is dropped when not using the first name. "von is German for "of"-- so its Helge of Koch..."of Koch" alone doesn't make as much sense. Lirath Q. Pynnor

 * I thought it was common to put the "von" in? As it's part of the name? In any case, if leaving it out is the Right Thing to do, then leave it out :) Dysprosia 00:22, 17 Nov 2003 (UTC)

There isn't a "right thing" to do; if you change it, Im not going to revert it -- both are used. Lirath Q. Pynnor

I've always seen it called the "Koch curve", not "von Koch"--70.245.253.65 02:00, 20 May 2006 (UTC)

the koch snowflake is quite ridiculous as it can have infinite perimeter but finite area

 * Congratulations. You just defined what a fractal is. --67.172.99.160 30 June 2005 21:01 (UTC)

 * Please sign your posts. Why do you call the Koch snowflake "ridiculous" implying that it has somehow earned your contempt? Its perimeter is not a line but instead a narrow probability distribution that challenges our usual ideas of perimeter or circumference that apply so easily to ordinary 2-D shapes such as circles, ellipses, polygons.Cuddlyable3 13:51, 17 April 2007 (UTC)

Koch curve / Koch snowflake
I'd consider it odd that Koch snowflake redirects here when the article itself states:
 * The better known Koch Snowflake (or Koch Star) is the same as the curve,[...]

How about a move to Koch snowflage (or Koch Star) and, if needed, a slight re-write of the article in order to make it suitable for the new location? Jobjörn 02:06, 25 February 2006 (UTC)

SEPARATE THE CURVE AND THE SNOWFLAKE!
 * Yes. Please. ErkDemon (talk) 13:37, 12 August 2019 (UTC)
 * They are not separable. The snowflake is just the subjective impression of 3 Koch curves. Cuddlyable3 18:45, 19 February 2007 (UTC)

 * Of course they are separable. The Koch Curve is an open shape that doesn't look remotely like a snowflake and only has reflective symmetry, the "Koch Snowflake" or "Koch Island" is a closed shape with reflective and rotational symmetry, and ... due to it's sixfold symmetry (normal snowflakes have sixfold symmetry) ... looks like a snowflake. The Snowflake has area, the curve doesn't. To say that "Koch curve" means "Koch snowflake" is to corrupt the meanings of technical terms - what then happens if a researcher want to refer specifically to the actual curve and not to the snowflake? What happens if WP has told everyone that there's no such thing as a Koch Curve that isn't the snowflake?

 * I think this is very, very bad. One might as well say that a cube is simply a shape assembled from squares, that WP's Square page should be deleted and redirect to Cube, and the Cube page should then explain that there's no difference between a square and a cube, and that a tetrahedron, which is related to a cube by being a variation on a different theme (Platonic solids), therefore also ought to be described as a variation on a square (facepalms). It's not just technically wrong ... its actually stupid. ErkDemon (talk) 13:37, 12 August 2019 (UTC)

I agree that the two are not separable, but the article is a bit confusing with alternating talk of curve/snowflake. Someone should clean it up a bit. By the way, Koch defined only the curve and every old math text I've read only references the curve. Other sites (like Wolfram) make the error of thinking Koch dreamed up the snowflake in 1904, but I've read the article and he didn't. Who first came up with the idea of putting 3 curves together to make a "snowflake" and when? --seberle (talk) 20:02, 23 January 2009 (UTC)

 * Another excellent reason for separating the two subjects. If we want to explain that Koch invented the curve but not the snowflake, then this is kinda difficult if the page says that Koch Curve means Koch Snowflake. Also, consider the 3D extension of the Koch Curve that I uploaded - it's not a 3D extension of the Koch snowflake, and technically shouldn't be on the snowflake page! The same goes for the other shapes in the "Variants of the Koch curve" section - some of them are examples of open curves and not snowflake-like objects, and ought to be in a separate page. In fact, you could pretty much split the page into two at this point.

 * There seems to be a very bad theme developing on WP fractals pages, where people decide to merge a range of different related subjects onto a single page. This is bad because it imposes a single way of sorting the data into groups, which prevents other potential groupings. The appropriate thing to do is to keep the individual entries separate, and for any "editorial overviews" for how they may be grouped to be done on separate category pages. If you put all these different variations onto the same page and delete the originals, it means that we can no longer include Koch Curve under "linear fractals" and Koch Snowflake under "fractals with area". We can no longer apply separate "date discovered" categories, we can't include some shapes under "fractal antennae" and not others, we can't sort by symmetry types, or rotational symmetry class.
 * The way things are now, it's like not only saying "Hey, the subject of squares can't be separated from the subject of cubes, so we don't need a separate page on Square", but then going further and saying "... And the construction of a triangle is kindoffa variation on the way of making a square, so we'll delete the page on Triangle and make that a subsection of the Cube page, too." ErkDemon (talk) 13:40, 12 August 2019 (UTC)

What actually is the Koch curve?
I understand the sequence of curves but don't understand what is meant by saying the Koch curve is the "limit" of these curves. Is the Koch curve a subset of the plane? Is it the set of all points that are eventually always members of the curves in the sequence? Or something else? Is it a mathematical curve, a continuous function from [0,1] to the plane? If someone knows, it would be good if they could add that information to the article. Count Truthstein (talk) 18:16, 14 December 2008 (UTC)
 * See Limit (mathematics). --92.37.88.76 (talk) 23:45, 20 December 2008 (UTC)
 * Well, it basically means that the "triangles" converge to the Koch curve - they approach it. --92.37.88.76 (talk) 23:47, 20 December 2008 (UTC)
 * I am fully aware of the definition of a limit. Each step in the sequence is a subset of the plane R^2 and I don't know of any standard way of defining a metric on P(R^2). Moreover if you did then we'd still have to say what the Koch curve is that it we claim it is tending to.
 * I don't think it's very likely that it's done that way. Another way would be to view the steps in the sequence as functions from [0,1] to R^2, where there are sensible choices for metrics. However the limit could depend on the choices of the functions that represent the curves in the sequence. There are multiple ways of choosing these functions, because if f:[0,1]->R^2 is a path (injective continuous function), and g is a strictly increasing continuous bijection [0,1]->[0,1] then the image of (f.g) is the same as the image of f. Count Truthstein (talk) 02:53, 27 December 2008 (UTC) (edited 17:12, 27 December 2008 (UTC))
 * Koch (1904) defined his function (after defining the curve) from the initial segment to the final curve by drawing a perpendicular from any point x on the initial segment and seeing where it first intersects any segment from any iteration. If that intersection is part of the final curve, fine; you're done. If not, draw a perpendicular from that second segment and see where it next intersects a segment from another iteration. And so on. Eventually you either hit the curve, or you have a convergent sequence of segments whose limit point is on the final curve. Either way, you have a mapping from x to a point f(x) on the Koch curve. --seberle (talk) 19:57, 23 January 2009 (UTC)

Countable / uncountable
Does the Koch curve have a countably infinite or an uncountably infinite number of sides? My gut says latter but I can't for the life of me figure it out formally. -pinkgothic (talk) 00:46, 1 April 2009 (UTC)

 * Well, things that grow in an exponential manner tend to be uncountable; some version of diagonal method often works well enough to prove it. Here for instance, assume contrarily that you can order all the "sides" in a sequence {A_n}. You can now recursively construct a "side" that, for each i, is contained in a different side of an ith generation curve than A_i is. This freshly constructed one by definition doesn't appear anywhere in the sequence. Contradiction.

 * The above is still not quite formal, because I am not sure what exactly do you mean by "sides" in this context. (Note that Koch Curve isn't differentiable anywhere!) But if you can formalise this notion somehow, the proof should work. 89.78.167.95 (talk) 09:11, 15 April 2009 (UTC)

 * As said above, there are no "sides" in the Koch curve, which is the limit set of the Koch snowflake iterative process. Each generation in the Koch snowflake process introduces a number of new vertices which are points in the limit curve - the 0th generation introduces the three vertices of the original triangle; the 1st generation introduces the 9 points at the apex and base of each of the smaller triangles; the 2nd generation introduces 36 new points at the apex and base of 12 new triangles etc. The limit curve will contain a countable number of these "rational" points, as each one can be indexed by the generation at which it first appears, and then, say, counting clockwise around from the apex of the original triangle. But the limit curve also contains "irrational" points, which do not appear in any snowflake generation, but are the limit points of a sequence of "rational" points - a diagonal argument can be used to show that there are an uncountable number of these "irrational" points. A similar argument shows that there an uncountable number of points in the Cantor set, even though the end-points of the removed open intervals form a countable set. Gandalf61 (talk) 11:04, 15 April 2009 (UTC)

Convergence ?
Does the algorithm for construction eventually converge ? Is there a way to test whether a point is "on" the curve ? It seems that all the points keep changing, i.e. the points of the nth iteration curve seem to be potentially different from the (n+10)th iteration curve. I assume there must be convergence, otherwise it would make no sense to speak of "the curve", but a clarification (and ideally an understandable argument) would be good in the article ! —Preceding unsigned comment added by 84.74.106.187 (talk) 19:39, 21 August 2009 (UTC)

 * As with other sets created through infinite iteration, the object is the ideal form of the set, the infinitieth iteration. While the lines between points are redefined in each iteration, vertices are not removed, only added, so if a vertex is a member of the set in one iteration, it will also be a member of the infinitieth iteration. Eventually, all the points between two vertices will be removed from the set, except the neighboring points an infinitesimal distance away in the direction of the vertices that it connected to within its own iteration. Of course, testing for set membership with the generating algorithm will not allow you to confirm that a point isn't in the set, only that it is or isn't in the nth iteration of the set, just as with the Mandelbrot set. And of course, you can't determine if an algorithm will run forever or not. If there's a standard algorithm that can give a straight "no" for membership of the Koch curve, I don't know about it. LokiClock (talk) 11:42, 17 February 2010 (UTC)

 * Membership in the Koch fractal is decidable: Draw the fractal with line thickness $$t=a^{-n}$$. To ensure that the area covered by the line vanishes, choose $$a>4/3$$. If a point is not in the set, it will be a finite distance $$x$$ away, and will cease to lie on the line after a finite number of iterations. Together with the vertex detection method you can decide for any given point whether it is part of the fractal. Paradoctor (talk) 17:37, 17 February 2010 (UTC)

 * I'm having a little bit of trouble understanding the process as you're describing it. Do you have a link to somewhere where I can read about it in-depth? LokiClock (talk) 15:25, 18 February 2010 (UTC)

 * Sorry, no link, pulled that one out of what I jokingly call my mind. I'll write something hopefully readable later. Paradoctor (talk) 16:54, 18 February 2010 (UTC)

 * Here we go: Stated without proof: The Koch curve is compact. (IIRC, this is an exercise in some textbooks.) This means that every point that is the limit of a series of vertices is a part of the curve. This implies that all and only those points at a finite distance from all posible sequences of vertices are off the curve. Now start drawing the sequence of approximations, but decrease the line thickness by a constant factor for each iteration, 1/2 is enough. Since the line thickness becomes arbitrarily small, any point a finite distance away from the curve will cease to be covered by the line after finite number of iterations, and you'll know that the point is not on the curve.
 * Now comes the part where I apologize: Writing this, I realized that the property of being on the curve appears to be undecidable. There should be some argument from Rice's theorem, but I'm brain-drained right now. HTH, Paradoctor (talk) 21:35, 18 February 2010 (UTC)
 * Okay, are you saying to decrease the thickness of all the lines in each step, or only the new lines? If it's the former, I understand. And what is the difference exactly between a point being on the curve and a point being part of the fractal? LokiClock (talk) 13:54, 19 February 2010 (UTC)
 * I meant all lines, but it shouldn't make much of a difference. Remember that non-vertex points of the segments will be removed in later iterations.
 * We're talking about two different fractals. The curve has properties different from curve+interior. AFAIK, curve+interior is not compact, which makes a huge difference. Paradoctor (talk) 14:34, 19 February 2010 (UTC)
 * I see. So the compactness in this case determines the decidability? LokiClock (talk) 14:48, 19 February 2010 (UTC)

 * There may be a way of proving computability of non-membership without relying on compactness, but that question is beyon my ken. Paradoctor (talk) 15:13, 19 February 2010 (UTC)

Sphereflake
Besides the shape's idiosyncrasy (being sphere-packing-based), the bit about it is unsourced, claims a specific developer, and until I changed it put its name in bold. Is there any support for its notability or the particular choice of this article for its place of inclusion? LokiClock (talk) 14:46, 16 February 2010 (UTC)

 * According to : "Exercise 74: Sphereflake" (p545&566) in, I'll add more later. Paradoctor (talk) 15:08, 16 February 2010 (UTC)

Countable / Uncountable length
A couple of editors question whether the length is well defined. Surely it is as well defined as any limit of a divergent sequence? Some sources say the snowflake's perimeter has infinite length (e.g. the article's first external link: ). So is it countable or uncountable? The article should say one way or another. --Michael C. Price talk 20:22, 20 March 2010 (UTC)

 * The source listed by you does not look like an RS to me. The statement looks fishy to me, as per my edit summary. Note that some sets are not measurable. Also, it is not hard to construct a fractal set whose limit is the unit interval. Thich gives us a series of curves whose length goes to infinity, while its limit has a clearly defined finite length. If you can cite a couple of good sources talking about "infinite length", please add them. IMPO, this notion looks like a common misconception. Of course, I'm not a reliable source. ;) Paradoctor (talk) 21:01, 20 March 2010 (UTC)

 * I'm puzzled by the link you provided. What's its relevance?  The link I posted was from the article; if it isn't reliable (and here's a better source, BTW, that states the Koch curve has infinite length) then what was it doing in the article? If the Koch perimeter is not measurable then I presume the Menger sponge also doesn't have an infinite area, yet it is desribed: The Menger sponge simultaneously exhibits an infinite surface area and encloses zero volume. .--Michael C. Price talk 06:47, 21 March 2010 (UTC)

 * The link is the author's homepage. Doesn't really look like an authority to me. ;) His copyright notice is here.
 * "what was it doing in the article": Obviously, someone misjudged it's RSness.
 * Menger sponge: The statement is cited to an RS, that's what makes the difference. Also note that these are different fractals, I did not say that all fractals are unmeasurable. Please note that the limit of a sequence may have properties not shared with any members of the sequence. A simple example is the series $$a_n=2^{-n-1}$$. None of its members is an integer, yet the limit is. If you don't find that remarkable, check out 1 − 2 + 3 − 4 + ···, which can have a sum of $$1/4$$, depending on the summation method.
 * "better source": I'm afraid not. Skinner's page is part of a student project, and the teacher of the course stated "There were also a few real duds among these. You can decide for yourself which were which.", so we still have nothing solid to go on. Paradoctor (talk) 09:52, 21 March 2010 (UTC)

 * The concepts of countable and uncountable only apply to infinite sets. A line is a set of points (and even a line with finite length is an uncountable set of points) but the length of a line is not a set - it is an example of a measure. So it does not make sense to describe the length of a line as being countable or uncountable. The phrase "The Koch curve has an infinite length" is shorthand for saying that the lengths of the iterations that approach the Koch curve do not approach a finite limit. Gandalf61 (talk) 13:06, 21 March 2010 (UTC)
 * How many inches in an endless straight line (in Euclidean space)? --Michael C. Price talk 21:05, 21 March 2010 (UTC)

 * "as well defined as any limit of a divergent sequence": That one slipped past me. Divergent sequences have no limit, that is precisely what distinguishes them from convergent sequences. You might define a measure which permits infinite values, and then you can say that the sequence of lengths of the Koch curve approximations converges onto the limit value "infinite". But this is a property of the sequence, not necessarily of its limit. The problem is that you need to show that your definition of the measure "length" is applicable to the Koch curve. The Banach-Tarski paradox shows that you may not simply assume that all sets are measurable. That's why I'm asking for a reliable source. Paradoctor (talk) 15:09, 21 March 2010 (UTC)
 * From gscholar:
 * It follows that the Koch curve has infinite length
 * length of the Koch curve becomes infinite
 * the length of the limit curve is infinite Full PDF
 * extrapolates to give infinite length for the fractal curve
 * its border, a scaling fractal of infinite length
 * the actual length of a fractal curve between two points a finite distance apart is infinite
 * The Koch curve is self-similar at every scale and has, in the limit ... infinite length
 * Koch Snowflake(s) ... are of infinite length.
 * Any reliable? --Michael C. Price talk 21:28, 21 March 2010 (UTC)
 * Let me first compliment you for looking for sources rather than complaining, I get the latter far too often. ;)
 * The author is a professor of mathematics. Problem is, this is just a coursenote, nothing peer-reviewed, which is what we're looking for.
 * This author is an MD, this one is at least professor of biomathematics. It is not clear, though, that he vetted this particular statement. Also note that this is a physiology journal, not mathematics.
 * Mandelbrot in Science would clearly be an authoritative source. I need to see sufficient context to make sure that he didn't make this statement merely to knock it down. Do that, and we're done here. :) Don't get your hopse too high, though: "Geographical curves are so involved in their detail that their lengths are often infinite or, rather, undefinable."
 * The author has published some work in poweder physics. He did work on using fractals to describe the behavior of powders, but that doesn't make him an WP:RS for us, especially seeing as this work is now ~30 years old.
 * Good old Gardner. Not an RS, though I, like many, like his stuff.
 * Another physicist. International Journal of Fracture? ^_^
 * Chemical Engineering or geology, take your pick.
 * Lawyers? What has become of WP:LEGALTHREAT? ;)
 * Let me sum it up. We need either a journal article or a major textbook in mathematics competent on fractals and measures. So far, your best bets are the Mandelbrot article or finding a peer-reviewed paper by the first professor. Happy editing, Paradoctor (talk) 22:57, 21 March 2010 (UTC)
 * Full Mandelbrot PDF. The context is fine - he does not knock it down. --Michael C. Price talk 04:51, 22 March 2010 (UTC)

 * If you include the quote "Thus, the length of the limit curve is infinite, even though it is a “line.”" from page 637, you have found yourself a valid citation to an WP:RS. :) Don't use the link to the full PDF, though, it's a copyvio as it violates JSTOR's terms of use.

 * As Gandalf61 explained, it doesn't make sense to quantify the infiniteness of length as countable or uncountable, hence my edit. However, I agree with Michael that the curve has infinite length, not just that the lengths of the stages in the construction converges to infinity. Another source for this statement is The Princeton Companion to Mathematics, where it is explicitly stated (p. 184) that the Koch snowflake has infinite length. /Pontus (talk) 07:35, 22 March 2010 (UTC)
 * See my response to Gandalf61 for why I do not, yet ay least, accept his statement. Is the length of an infinite straight line itself infinite? Yes, if we measure with respect any unit of measurement. Now form a list of the unit lengths, and every part appears somewhere in the ordered list - therefore the length of a straight line is countable. For a Koch curve such a list is not constructible, therefore its length is uncountable? --Michael C. Price talk 11:07, 22 March 2010 (UTC)
 * Perhaps you mean that the 1-dimensional Hausdorff measure on the curve is not σ-finite? /Pontus (talk) 11:44, 22 March 2010 (UTC)
 * Neither a textbook, nor a peer-reviewed publication, even though written by experts. Please note that, IMHO, even the Mandelbrot paper is plain wrong. But it is an RS, and for our purposes far superior to the PCM, so the onus is on me to prove anything to the contrary. Cf. the first hit, which is an article in Chaos, Solitons & Fractals. Paradoctor (talk) 08:19, 22 March 2010 (UTC)
 * I would have thought that the PCM is a more reliable source than Mandelbrot. However, since they agree, it is not a problem.--Michael C. Price talk 11:07, 22 March 2010 (UTC)

Mathematics and the imagination
The Koch snowflake features prominently in chapter 9 of Mathematics and the Imagination. The chapter (pages 299 to 356) is called "Change and Changeability — The Calculus". The figures (#145 to #150) range over pages 345 to 350 showing the first six stages of the construction. On page 345 the authors say "Its pathological character is born out by this incredible feature ... the length of its perimeter is infinite." On page 347 they say, "...it is not possible to tell at any point on the limit curve the direction in which it is going, that is, the tangent line does not exist."

Instead of mounting the triangles on the outside, they may be taken from the interior of the preceding figure. The result is called the "Anti-Snowflake". The first four stages of the process is illustrated with figures #151 to #162 on page 351.

A space-filling curve is then introduced (pages 352,3) with figures #159 to #162.Rgdboer (talk) 19:58, 18 April 2011 (UTC)

Proof of area incomplete
Is it just me or is the proof of the area of the Koch snowflake missing the most interesting part: why do the little triangles never overlap? (In the similar problem http://www.artofproblemsolving.com/Forum/viewtopic.php?f=41&t=5333, they do overlap, so that the naive method of calculating the area fails.) -- Darij (talk) 22:28, 29 March 2012 (UTC)
 * You are right, the prof is not complete. Prokofiev2 (talk) 08:21, 30 March 2012 (UTC)

My proof may be too long but still worth considering
I expanded the proof of the area and perimeter of the snowflake but it was undone. I think that the explanation as it was is too short and doesn't really get you from point A to point B in the proof smoothly enough. What do the others think?

Here's my edit: http://en.wikipedia.org/w/index.php?title=Koch_snowflake&oldid=537408182

Mtanti (talk) 11:11, 10 February 2013 (UTC)

Who is it named after?
I think that discussing origin and creation circumstances would be appropriate for an article like this. At least a brief mention.174.56.55.37 (talk) 17:54, 23 July 2014 (UTC)

Nazi sign?

I wonder how long will it take until the US Congress recognise this sign as Neo-Nazi sign? Since they already called the Idea of Nation sign as one (see Azov Battalion). Aleksandr Grigoryev (talk) 22:57, 3 January 2017 (UTC)

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Why do we need 'Not to be confused with Dave Rubin'?
The Dave Rubin page doesn't contain any reference to Koch snowflakes and the name is not at all alike. The reference was added by 86.44.63.103 yesterday. Albert Pool (talk) 10:24, 30 November 2018 (UTC)
 * It is just vandalism. I have already reverted it. --Zupanto (talk) 19:01, 5 December 2018 (UTC)
 * The joke is that, since Dave Rubin is conservative/classical liberal/libertarian, "Koch" can be reinterpreted as the conservative/classical liberal/libertarian Koch Brothers and "snowflake" as the insult "snowflake". The reason why there are (presumably) three vandals with completely different IP addresses is that this page has been posted on the leftist sub-Reddit r/ChapoTrapHouse (named after the podcast) (at least) four times ( (the original vandal probably comes from here),, , (the (presumably) two reverters probably come from here)). --Zupanto (talk) 22:51, 5 December 2018 (UTC)

Semi-protected edit request on 24 January 2019
I would like to remove the completely irrelevant reference to Dave Rubin at the top of the page. DiabolikDownUnder (talk) 09:57, 24 January 2019 (UTC)
 * Yes check.svg Done – Jonesey95 (talk) 11:18, 24 January 2019 (UTC)

File:KochTurtleAnim.gif
The image File:KochTurtleAnim.gif (code: ) was removed from this article because its inclusion doesn't seem to add, "any understanding or useful information about this topic". However, some readers, especially highly visual learners, may get a deeper understanding through a small illustration or short animation than through a text description however lengthy. I think math content on Wikipedia should be accessible to all people and I assume that the creator of the animation thought that it would add either "understanding," or, "useful information," if not both. Hyacinth (talk) 03:42, 14 September 2019 (UTC)

Minkowski fractal
See the discussion at Wikipedia talk:WikiProject Mathematics#Minkowski fractal. Hyacinth (talk) 03:53, 14 September 2019 (UTC)

Image: SVG vs PNG
Which is preferable: File:Koch quadratic island L7 3.png or File:Koch quadratic island L7 3.svg? Hyacinth (talk) 02:13, 3 April 2020 (UTC)
 * For display within the article it makes no difference, but if we expect some viewers to click on the article image and look more carefully at it blown up then the svg is better (not least because when I try it in my browser I see the png displayed as a black shape with a transparent background displayed over black, so basically invisible). —David Eppstein (talk) 05:26, 3 April 2020 (UTC)

Area formula
The area formula could be made much simpler ... With original triangle of area a0, with 3 sides, we get additional area of 3*1/9*a0, and four times as many sides, so the next addition to the area is 3/9*4/9, and so on, to give a0 + a0*1/3*(4/9)^n-1. The second half of this expression is the formula for the nth term in a G.P. with 'a'= 1/3 and 'r'= 4/9. This has a sum given by the usual formula: 1/3 divided by (1 - 4/9), which straight away gives 3/5. Add in the original area and you have 8/5. Jerryfrog (talk) 04:50, 8 November 2023 (UTC)

Number of sides formula incorrect?
The articles says number of sides after n iterations is given by ... $$N_{n} = N_{n-1} \cdot 4 = 3 \cdot 4^{n-1}\, .$$

But on iteration 0 (the initial triangle) there are 3 sides, but the formula with n = 0 would give 3/4 of a side. Axlesoft (talk) 12:10, 21 February 2024 (UTC)

title: Talk:Koch snowflake


text:
Meat alternative

A meat alternative or meat substitute (also called plant-based meat, mock meat, or fake meat sometimes pejoratively), is a food product made from vegetarian or vegan ingredients, eaten as a replacement for meat. Meat alternatives typically approximate qualities of specific types of meat, such as mouthfeel, flavor, appearance, or chemical characteristics. Plant- and fungus-based substitutes are frequently made with soy (e.g. tofu, tempeh, and textured vegetable protein), but may also be made from wheat gluten as in seitan, pea protein as in the Beyond Burger, or mycoprotein as in Quorn. Alternative protein foods can also be made by precision fermentation, where single cell organisms such as yeast produce specific proteins using a carbon source; as well as cultivated or laboratory grown, based on tissue engineering techniques.

Meatless tissue engineering involves the cultivation of stem cells on natural or synthetic scaffolds to create meat-like products. Scaffolds can be made from various materials, including plant-derived biomaterials, synthetic polymers, animal-based proteins, and self-assembling polypeptides. It is these 3D scaffold-based methods provide a specialized structural environment for cellular growth. Alternatively, scaffold-free methods promote cell aggregation, allowing cells to self-organize into tissue-like structures.

Meat alternatives are typically consumed as a source of dietary protein by vegetarians, vegans, and people following religious and cultural dietary laws. However, global demand for sustainable diets has also increased their popularity among non-vegetarians and flexitarians seeking to reduce the environmental impact of animal agriculture.

Meat substitution has a long history. Tofu was invented in China as early as 200 BCE, and in the Middle Ages, chopped nuts and grapes were used as a substitute for mincemeat during Lent. Since the 2010s, startup companies such as Impossible Foods and Beyond Meat have popularized pre-made plant-based substitutes for ground beef, patties, and vegan chicken nuggets as commercial products.

History

Tofu, a meat alternative made from soybeans, was invented in China by the Han dynasty (206 BC–220 CE). Drawings of tofu production have been discovered in a Han dynasty tomb. Its use as a meat alternative is recorded in a document written by Tao Gu (, 903–970). Tao describes how tofu was popularly known as "small mutton", which shows that the Chinese valued tofu as an imitation meat. Tofu was widely consumed during the Tang dynasty (618–907), and likely spread to Japan during the later Tang or early Song dynasty.

In the third century CE, Athenaeus describes a preparation of mock anchovy in his work Deipnosophistae:

Wheat gluten has been documented in China since the sixth century. The oldest reference to wheat gluten appears in the Qimin Yaoshu, a Chinese agricultural encyclopedia written by Jia Sixie in 535. The encyclopedia mentions noodles prepared from wheat gluten called bo duo. Wheat gluten was known as mian jin by the Song dynasty (960–1279).

Prior to the arrival of Buddhism, northern China was predominantly a meat-consuming culture. The vegetarian dietary laws of Buddhism led to development of meat substitutes as a replacement for the meat-based dishes that the Chinese were no longer able to consume as Buddhists. Meat alternatives such as tofu and wheat gluten are still associated with Buddhist cuisine in China and other parts of East Asia. Meat alternatives were also popular in Medieval Europe during Lent, which prohibited the consumption of warm-blooded animals, eggs, and dairy products. Chopped almonds and grapes were used as a substitute for mincemeat. Diced bread was made into imitation cracklings and greaves.

John Harvey Kellogg developed meat replacements variously from nuts, grains, and soy, starting around 1877, to feed patients in his vegetarian Battle Creek Sanitarium. Kellogg's Sanitas Nut Food Company sold his meat substitute Protose, made from peanuts and wheat gluten. It became Kellogg's most popular product as several thousand tons had been consumed by 1930.

There was an increased interest in meat substitutes during the late 19th century and first half of the 20th century. Prior to 1950, interest in plant-based meat substitutes came from vegetarians searching for alternatives to meat protein for ethical reasons, and regular meat-eaters who were confronted with food shortages during World War I and World War II.

Lentils were used at the turn of the century. In 1897, Food, Home and Garden published a positive review of London's vegetarian restaurants, claiming, "For fivepence one could get a lentil cutlet, which was very appetizing, and looked like a meat croquette".

Henrietta Latham Dwight authored a vegetarian cookbook, The Golden Age Cook-Book in 1898 which included meat substitute recipes such as a "mock chicken" recipe made from breadcrumbs, eggs, lemon juice and walnuts and a "mock clam soup" made from marrowfat beans and cream. Dietitian Sarah Tyson Rorer authored the cookbook, Mrs. Rorer's Vegetable Cookery and Meat Substitutes in 1909. The book includes a mock veal roast recipe made from lentils, breadcrumbs and peanuts. In 1943, Kellogg made his first soy-based meat analog, called Soy Protose, which contained 32% soy. In 1945, Mildred Lager commented that soybeans "are the best meat substitute from the vegetable kingdom, they will always be used to a great extent by the vegetarian in place of meat."

In July 2016, Impossible Foods launched the Impossible Burger, a beef substitute which claims to offer appearance, taste and cooking properties similar to meat. In April 2019, Burger King partnered with Impossible Foods to launch the plant-based Impossible Whopper, which was released nationwide later that year, becoming one of the most successful product launches in Burger King's history. By October 2019, restaurants, such as Carl's Jr., Hardee's, A&W, Dunkin' Donuts, and KFC were selling plant-based meat products. Nestlé entered the plant-based burger market in 2019 with the introduction of the "Awesome Burger". Kellogg's Morningstar Farms brand tested its Incogmeato line of plant-based protein products in early September 2019, with plans for a US-wide rollout in early 2020.

Types
Some vegetarian meat alternatives are based on centuries-old recipes for seitan (wheat gluten), rice, mushrooms, legumes, tempeh, yam flour or pressed-tofu, with flavoring added to make the finished product taste like chicken, beef, lamb, ham, sausage, seafood, etc. Other alternatives use modified defatted peanut flour, yuba and textured vegetable protein (TVP); yuba and TVP are both soy-based meat alternatives, the former made by layering the thin skin which forms on top of boiled soy milk, and the latter being a dry bulk commodity derived from soy and soy protein concentrate. Some meat alternatives include mycoprotein, such as Quorn which usually uses egg white as a binder. Another type of single cell protein-based meat alternative (which does not use fungi however but rather bacteria ) is Calysta.

Production and composition
To produce meat alternatives with a meat-like texture, two approaches can be followed: bottom-up and top-down. With bottom-up structuring, individual fibers are made separately and then assembled into larger products. An example of a meat alternative made using a bottom-up strategy is cultured meat. The top-down approach, on the other hand, induces a fibrous structure by deforming the material, resulting in fibrousness on a larger length scale. An example of a top-down technique is food extrusion.

Both bottom-up and top-down processing can be used alone or in combination to offer various benefits. As discussed later, different meat alternative products have varying nutritional values. A notable advantage of the bottom-up approach is its ability to provide precise control over the composition and characteristics of the end product, allowing for optimized nutritional profiles. On the other hand, meat alternatives produced by top-down approaches may have limited malleability but are more scalable and can utilize available agricultural resources and infrastructure effectively. According to a study by Wageningen University & Research titled "Structuring Processes for Meat Analogues," Techniques that follow the bottom-up strategy have the potential to resemble the structure of meat most closely.". A cross-national survey conducted among meat-eaters with varying degrees of meat alternative consumption showed that those who consumed higher quantities of meat were more willing to switch to meat alternatives if they resembled authentic meat more accurately. Which can be accomplished through bottom-up approaches. The study concludes that sensory experience plays a crucial role in utilizing plant-based alternatives for heavy meat eaters.

The types of ingredients that can be used to create meat substitutes is expanding, from companies like Plentify, which are using high-protein bacteria found in the human microbiome, to companies like Meati Foods, that are cultivating the mycelium of fungi—in this case, Neurospora crassa—to form steaks, chicken breasts, or fish.

Soy protein isolates or soybean flour and gluten are usually used as foundation for most meat substitutes that are available on the market. Soy protein isolate is a highly pure form of soy protein with a minimum protein content of 90%. The process of extracting the protein from the soybeans starts with the dehulling, or decortication, of the seeds. The seeds are then treated with solvents such as hexane to extract the oil from them. The oil-free soybean meal is then suspended in water and treated with alkali to dissolve the protein while leaving behind the carbohydrates. The alkaline solution is then treated with acidic substances to precipitate the protein, before being washed and dried. The removal of fats and carbohydrates results in a product that has a relatively neutral flavor. Soy protein is also considered a "complete protein" as it contains all of the essential amino acids that are crucial for proper human growth and development.

After the textured base material is obtained, a number of flavorings can be used to give a meaty flavor to the product. The recipe for a basic vegan chicken flavor is known since 1972, exploiting the Maillard reaction to produce aromas from simple chemicals. Later understanding of the source of aroma in cooked meat also found lipid oxidation and thiamine breakdown to be important processes. By using more complex starting materials such as yeast extract (considered a natural flavoring in the EU), hydrolyzed vegetable protein, various fermented foods, and spices, these reactions are also replicated during cooking to produce richer and more convincing meat flavors.

Commerce
Meat substitutes represent around 11% of the world's meat and substitutes market. As shown in the graph, this market share is different from region to region. From 2013 to 2021, the world average price of meat substitutes fell continuously, by an overall 33%. The only exception was a 0.3% increase in 2020, compared to 2019. The price will continue to decrease, according to projections by Statista (see average price graph).

The motivation for seeking out meat substitutes varies among consumers. The market for meat alternatives is highly dependent on "meat-reducers", who are primarily motivated by health consciousness and weight management. Consumers who identify as vegan, vegetarian or pescetarian are more likely to endorse concerns regarding animal welfare and/or environmentalism as primary motivators. Additionally, some cultural beliefs and religions place prohibitions on consuming some or all animal products, including Hinduism, Judaism, Islam, Christianity, Jainism, and Buddhism.

Vegan meats are consumed in restaurants, grocery stores, bakeries, vegan school meals, and in homes. The sector for plant-based meats grew by 37% in North America over 2017–18. In 2018–19, sales of plant-based meats in the United States were $895 million, with the global market for meat alternatives forecast to be $140 billion by 2029. Seeking a healthy alternative to meat, curiosity, and trends toward veganism were drivers for the meat alternative market in 2019. Sales of plant-based meats increased during the COVID-19 pandemic. The book The End of Animal Farming by Jacy Reese Anthis argues that plant-based food and cultured meat will completely replace animal-based food by 2100.

Environmental
Besides ethical and health motivations, developing better meat alternatives has the potential to reduce the environmental impact of meat production, an important concern given that the global demand for meat products is predicted to increase by 15 percent by 2031. Research on meats and no-meat substitutes suggests that no-meat products can offer substantial benefits over the production of beef, and to a lesser extent pork and chicken, in terms of greenhouse gas production, water and land use. A 2022 report from the Boston Consulting Group found that investment in improving and scaling up the production of meat and dairy alternatives leads to big greenhouse gas reductions compared with other investments.

According to The Good Food Institute, improving efficiency of the Western diet is crucial for achieving sustainability. As the global population grows, the way land is used will be reconsidered. 33% of the habitable land on Earth is used to support animals. Of all the land used for agriculture, 77% is used on animal agriculture even though this sector only supplies 17% of the total food supply. Plant-based meat can use a potential 47–99% less land than conventional meat does, freeing up more opportunities for production. Of the total water used in global agriculture, 33% goes to animal agriculture while it could be used for drinking water or other growing purposes under a different strategy. Plant-based meat uses 72–99% less water than conventional meat production.

Pollution is the next largest contribution to wasted water. Pesticides used in animal feed production as well as waste runoff into reservoirs can cause ecological damage and even human illness as well as taking water directly out of the usable supply. Animal agriculture is the main contributor to the food sector greenhouse gas emissions. Production of plant-based meat alternatives emits 30–90% less than conventional meat production. While also contributing less to this total pollution, much of the land being used for animal feed could be used to mitigate the negative effects we've already had on the planet through carbon recycling, soil conservation, and renewable energy production. In addition to the ecological harm caused by the current industry, excess antibiotics given to animals cause resistant microbes that may render some of the life-saving drugs used in human medicine useless. Plant-based meat requires no antibiotics and would greatly reduce microbe antibiotic resistance.

A 2023 study published in Nature Communications found that replacing just half of the beef, chicken, dairy and pork products consumed by the global population with plant-based alternatives could reduce the amount of land used by agriculture by almost a third, bring deforestation for agriculture nearly to a halt, help restore biodiversity through rewilding the land and reduce GHG emissions from agriculture by 31% in 2050, paving a clearer path to achieving both climate and biodiversity goals. The switch to plant-based protein is reported to deliver the biggest climate-heating emission cuts per investment dollar of all industrial sectors.

Health
Meat alternatives have lower amounts of saturated fat, vitamin B12 and zinc than meat products but higher amounts of carbohydrates, dietary fibre, sodium, iron and calcium.

In 2021, the American Heart Association stated that there is "limited evidence on the short- and long-term health effects" of plant-based meat alternatives. The same year, the World Health Organization stated that there are "significant knowledge gaps in the nutritional composition" of meat alternatives and more research is needed to investigate their health impacts.

A 2023 review concluded that replacing red and highly-processed meat with a variety of meat alternatives improved quality-adjusted life years, led to significant health system savings and reduced greenhouse gas emissions; replacement of meat with minimally-processed vegetarian alternatives, such as legumes had the greatest effect.

A 2024 review found that plant-based meat alternatives have the potential to be healthier than animal source foods and have smaller environmental footprints.

Criticism
Companies producing plant-based meat alternatives, including Beyond Meat and Impossible Foods, have been criticized for their marketing and makeup of their products as well as their use of animal testing. Dietitians have claimed they are not necessarily healthier than meat due to their highly processed nature and sodium content.

John Mackey, co-founder and CEO of Whole Foods, and Brian Niccol, CEO of Chipotle Mexican Grill, have criticized meat alternatives as ultra-processed foods. Chipotle has claimed it will not carry these products at their restaurants due to their highly processed nature. CNBC wrote in 2019 of Chipotle joining "the likes of Taco Bell ... and Arby's in committing to excluding meatless meats on its menu." In response, Beyond Meat invited Niccol to visit its manufacturing site to see the production process. Chipotle later developed its own "plant-based chorizo". In September 2022, Taco Bell also began adding plant-based meat alternatives to its menu.

Some consulting firms and analysts demand more transparency in terms of the environmental impact of plant-based meat. Through a survey, analysts from Deloitte discovered that some consumers negatively linked meat alternatives to being "woke" and politically-left leaning. These ideas emerged in response to Cracker Barrel's introduction of Impossible Sausages in their restaurants in August, 2022. In 2021, 68% of consumers who purchased plant based meats believed it was healthier than animal meat. The number dropping to 60% in 2022, demonstrating a decline in consumers beliefs in the healthiness of these meats.

Some states have instituted legislation stating that meat alternatives are not allowed to label themselves as "meat". In Louisiana, the so-called, "Truth in Labeling of Food Products Act" was challenged by Tofurky, complaining of free speech violations and was successful on those grounds.

Alternative meats companies Beyond Meat and Impossible Foods have attempted to appeal to meat eaters. University of Oregon marketing professor Steffen Jahn thinks that this has run afoul of human psychology, saying "the mimicking of real meat introduces that comparison of authenticity." Jahn argues that marketing plant-based meats with traditional meats leads to an artificiality that many consumers do not love. Consumer psychologists split foods into categories of "virtue" and "vice" foods, which ultimately guide how products are marketed and sold. Virtue foods are those that less gratifying appealing in the short term, and typically healthier, whereas vice foods are the opposite, having more long term consequences. Many ready-made meat alternatives combine these categories with their long list of ingredients. Consumers who are likely to want to be "virtuous" by avoiding damage to the environment or animals are also likely to want "virtuous" food in the form of simple ingredients.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Meat alternative


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Talk:Simone Melchior

Redirects
How do I edit the search to p/u Simone Cousteau, Simone Melchior, Simone Melchior Couteau??jo

You can't edit the search as such, but what you can do is create redirects. Create a new page with the title Simone Cousteau for example, and then type in  #redirect Simone Melchior .

The page will automatically go to the Simone Melchior page, and Google will pick it up, so that if anyone searches for Simone Couteau they will be shown the Simone Melchior page. Don't go overboard and create loads though as you don't want to end up cluttering the search so it becomes less useful. Angela 02:17, 17 Nov 2003 (UTC)

Birth
I have much more info, but surprising, I don't have her Birthday or Birth Place. Can anyone help? Should I put a blank space where I want to put the info when I get it? Jo.G 16:39, Nov 17, 2003 (UTC)

It's probably best not to leave a space. The biographies section of the manual of style tells people where information like the date of birth should go anyway should anyone have this information. Angela 19:51, 17 Nov 2003 (UTC)

French language article
How would I go about translating this page into French? There are many people who knew Simone who speak french. I want their input.Jo.G 01:31, Nov 20, 2003 (UTC)

 * Well, the French version wouldn't be used on this Wikipedia, but if you wanted to do a translation, you could go to the French Wikipedia (http://fr.wikipedia.org). There isn't yet an article on Simone Melchior, though there is one on fr:Jacques-Yves Cousteau. If you want to ask French speakers to help with the translation, their version of the Village pump is at fr:Wikipédia:Le Bistro. Once there is such an article, you can link it to this one by writing Simone Melchior on this page which provides an interlanguage link. Angela 06:43, 20 Nov 2003 (UTC)

This Wiki stuff is fascinating. Thanks for the info. You know all the angles! Jo.G 18:21, Nov 20, 2003 (UTC)

Stub
How do I de-stub this work in progress? I think it is pretty concise and will only grow.Jo.G 14:51, Dec 12, 2003 (UTC)

Incorrect age or ages
''Simone met her future husband, Jacques, at a cocktail party in 1937. He was a naval officer of 25 and she was 17.'' He was born in June 1910, so he was either 26 or 27 when they met. --Espoo (talk) 15:27, 10 February 2008 (UTC)

Death
The article lacks her date and place of death; it only states the year. Biographies 2 (talk) 01:55, 12 June 2009 (UTC)

Please translate this page in German!
A new film about her husband Jacques-Yves Cousteau is now in the german cinemas and there is no german wiki page about Simone Melchior Cousteau! AugspurgII (talk) 11:39, 5 January 2017 (UTC)

title: Talk:Simone Melchior


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Sequence (disambiguation)

A sequence, in mathematics, is an ordered list of elements.

Sequence may also refer to:

Film

 * Sequence (filmmaking), a series of shots or scenes, edited together in succession
 * Sequence (journal), a film journal
 * Séquences, a Quebec film magazine
 * Sequence (2013 film), a 2013 short fantasy horror film
 * Sequence, a 16 minute film directed by David Winning

Games

 * Sequence (game), a board-and-card game distributed by Jax Ltd., Inc.
 * Before the Echo, a video game also known as Sequence

Music

 * Sequence (music), a passage which is successively repeated at different pitches
 * Sequence (musical form), a medieval Latin poem or its musical setting which became part of the Mass
 * The Sequence, a 1980s all-female hip-hop/funk trio

Biology and medicine

 * Sequence (biology), the primary structure of a biopolymer
 * Sequencing, determining the primary structure of an unbranched biopolymer
 * DNA sequencing, determining the order of the nucleotide bases in a DNA molecule
 * Protein sequencing
 * Primary sequence, the sequence of a biological macromolecule
 * Sequence analysis
 * Sequence (medicine), a series of ordered consequences due to a single cause

Other uses in science, technology, and mathematics

 * Sequence (geology), a succession of geological events
 * Archaeological sequence
 * Sequence diagram, used to visualise the design of a computing system
 * Sequential manual transmission, a type of manual automotive transmission
 * Sequence of events, a time-related notion in physics and metaphysics
 * Sequences (book), mathematics book by Heini Halberstam and Klaus Roth
 * List (abstract data type)
 * A rarely used programming language
 * A term for a pair of sprites

Other uses

 * Sequence of tenses, in grammar

title: Sequence (disambiguation)


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Lemuel Gulliver

Lemuel Gulliver is the fictional protagonist and narrator of Gulliver's Travels, a  novel written by Jonathan Swift, first published in 1726.

In Gulliver's Travels
According to Swift's novel, Gulliver was born in Nottinghamshire c. 1661, where his father had a small estate; the Gulliver family is said to have originated in Oxfordshire, however. He supposedly studied for three years (c. 1675–1678) at Emmanuel College, Cambridge, leaving to become an apprentice to an eminent London surgeon; after four years (c. 1678–1682), he left to study at the University of Leiden, a prominent Dutch university and medical school. He also educated himself in navigation and mathematics, leaving the university around 1685.

Prior to the voyages whose adventures are recounted in the novel, he is described as having travelled less remarkably to the Levant (c. 1685–1688) and later to the East Indies and West Indies (c. 1690–1696). In Brobdingnag, he compares a loud sound to the Niagara Falls, so presumably, he visited the place at some point. Between his travels, he married Miss Mary Burton (c. 1688), daughter of a London hosier. As of the time of his return from Lilliput, they had a son named Johnny, studying at grammar-school, and a daughter named Betty, married with children by the time Lemuel wrote his memoirs. Mary was pregnant with another child by the time her husband left on his last voyage. In his education and travels, Gulliver acquired some knowledge of "High and Low Dutch, Latin, French, Spanish, Italian, and Lingua Franca"; he later states that he understood some Greek and that he "understood (Portuguese) very well".

Gulliver's remarkable travels begin in 1699 and end in 1715, having changed Gulliver's personality to that of a recluse. He claims to have written his memoirs five years following his last return to England, i.e., in 1720 or 1721. The frontispiece to the 1726 edition of Gulliver's Travels shows a fictitious engraving of Gulliver at the age of 58 (i.e., c. 1719). An additional preface, attributed to Gulliver, added to a revised version of the work is given the fictional date of April 2, 1727, at which time Gulliver would have been about 65 or 66 years old. The earliest editions of the book credited Gulliver as the author, whom many at the time believed to be a real person. Swift, an Anglican clergyman, had published much of his work anonymously or pseudonymously.

In sequels and spinoffs

 * Hungarian writer Frigyes Karinthy reused Gulliver as the protagonist of two novels recounting his further travels, Voyage to Faremido (1916) and Capillaria (1921). Both stay true to the character as a surgeon with a wife and children, but transpose their plot (and retroactively Gulliver's four earlier travels) to the then-contemporary years leading up to, during, and after World War I.
 * In the 2007 comic The League of Extraordinary Gentlemen: Black Dossier by Alan Moore, Gulliver is the leader of the second incarnation of The League of Extraordinary Gentlemen in the 18th century, which then consists of The Scarlet Pimpernel and his wife Lady Blakeney, Fanny Hill (with whom Gulliver has been romantically involved), Dr Syn aka The Scarecrow, Nathaniel Bumppo and Orlando. Gulliver leads the League until his death of testicular cancer in 1799 and is buried in Lilliput. This version of Gulliver is evidently at least a generation younger than Swift's Gulliver; his dates have evidently been shifted forward in time to allow him to interact with other fictional characters of the later 18th century.
 * Gulliver is mentioned throughout the recent Malplaquet trilogy of children's novels by Andrew Dalton.  Taking much of their initial inspiration from T.H. White's Mistress Masham's Repose, the books describe the adventures of a large colony of Lilliputians living secretly in the enormous and mysterious grounds of an English country house (Stowe House in Buckinghamshire). In The Temples of Malplaquet, for example, Jamie Thompson (their human protector, aged 13) has a dream-like vision of the episode in which Gulliver is first captured by the Lilliputians.
 * In the Gulliver's Travels film released in 2010, Gulliver, played by Jack Black, is a mail room worker who fancies himself a writer but plagiarizes most of his work from the Internet. After Gulliver is assigned to write a story about the Bermuda Triangle, his ship becomes lost at sea and he finds himself in Lilliput.

In astronomy
On Mars's largest moon, Phobos, the crater Gulliver is named after him, while the crater Grildrig has the name given to Gulliver by the farmer's daughter Glumdalclitch in Brobdingnag, because of Swift's 'prediction' of the two then undiscovered Martian moons, which his Laputan astronomers had discovered.

title: Lemuel Gulliver


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User talk:Adhoert

I am anthony morris

title: User talk:Adhoert


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Scott Adams (game designer)

Scott Adams (born July 10, 1952) is an American entrepreneur, computer programmer, and video game designer. He co-founded, with then-wife Alexis, Adventure International in 1979. The company developed and published video games for home computers. The cornerstone products of Adventure International in its early years were the Adventure series of text adventures written by Adams.

Adventure International

Born in Miami, Florida, Adams had access to an advanced 16-bit computer at home, built by his brother Richard Adams, that gave him a jump on game programming in his leisure time. Adams wrote a graphical action game similar to Spacewar! on this system in 1975.

Scott Adams was the first person known to create an adventure-style game for personal computers, in 1978 on a 16 KB Radio Shack TRS-80 Model I, written in BASIC. Colossal Cave was written two years earlier by Will Crowther, but on a mainframe computer (the PDP-10). These early text adventures recognize two-word commands of the form VERB NOUN. The parser only scans the first three letters of each command, so SCREAM BEAR, SCRATCH BEAR, or SCREW BEAR are treated identically. The games from his company, Adventure International, were subsequently released on most of the major home computers of the day, including TRS-80, Exidy Sorcerer, Apple II, Atari 8-bit computers, PET, VIC-20, and ZX Spectrum. Later adventure games added graphics, with the text entry window below an image illustrating the scene.

Adams's work was influential in adventure gaming. In 1990 Computer Gaming World reported a statement by a "respected designer" that it was impossible to design new and more difficult adventure puzzles, because Adams had already created them all in his early games.

Adams and his wife eventually started organizing their own conventions, and opened a chain of computer stores in Orlando. Alexis negotiated the rights to make a video game out of the Buckaroo Banzai sci-fi movie in 1983.

Later work
Since the late 1980s, Scott Adams has worked as a senior programmer for AVISTA in Platteville, Wisconsin.

In 2013, Scott Adams released the Bible-based The Inheritance, his first game in over ten years. As in most of his other games, the player is the protagonist of a novel-like story and helps events unfold in a text adventure set. However, this new game also includes sound. In a 2018 interview Adams said he had not been happy with the game as it was released so had withdrawn it from the market whilst it was rewritten.

In July 2016, Adams created a new company called Clopas to begin publishing games in a new genre he called "Conversational Adventure Games". These games were similar to his early text adventure games, except that they now supported full natural language sentences. The first game he put out under company was Escape The Gloomer, a game published in collaboration with Soma Games for their  Lost Legends of Redwall series.

Personal life
Adams met Irene "Alexis" Reuben in 1977 and they married not long after. While at first she only saw his computer obsession as something that prevented them from sharing more time together, already when pregnant with the couple's first child Alexis Adams saw the business potential of personal computer adventure games, and they started their company as co-founders. Adams would describe how his wife "handles most of the business" as the corporate vice president and general manager of Adventure International, and that she "has been intimately involved in all aspects... from the very beginning".

The couple decided to build an image of mystery around their company and opted to put Scott's name alone on products. Still Alexis was credited as co-creator on some games' title screens, with one giving her sole billing: Voodoo Castle (1979). In a 1980 interview, Scott credited his wife with using his tools to create 95% of that game by herself. One character from that game, "Medium Maegen" named after the couple's daughter, may be the first woman with dialogue in a video game, appearing years before most other contenders.

Scott and Alexis divorced not long after the video game crash of 1983. Alexis died in 2008, 51 years old.

Adams later remarried.

Adventure International

 * Adventureland (1978)
 * Pirate Adventure (1979)
 * Secret Mission (1979)
 * Voodoo Castle (1979) in collaboration with Alexis Adams
 * The Count (1979)
 * Strange Odyssey (1979)
 * Mystery Fun House (1979)
 * Pyramid of Doom (1979) in collaboration with Alvin Files
 * Ghost Town (1980)
 * Savage Island, Part I (1981)
 * Savage Island, Part II (1981) in collaboration with Russ Wetmore
 * Golden Voyage (1981) in collaboration with William Demas
 * Sorcerer of Claymorgue Castle (1982)
 * Return to Pirate's Isle (1983) exclusively for the TI-99/4A
 * Questprobe #1: The Hulk (1984)
 * Questprobe #2: Spider-Man (1984)
 * Questprobe #3: The Fantastic Four (1984)
 * The Adventures of Buckaroo Banzai Across the 8th Dimension (1984) in collaboration with Phillip Case

Later

 * Scott Adams Scoops (1987) collection of earlier games published by U.S. Gold
 * Return to Pirate's Island 2 (August 2000)
 * The Inheritance (February 14, 2013)
 * The Lost Legends of Redwall: Escape the Gloomer (2018)

Unreleased

 * Questprobe #4: X-Men

title: Scott Adams (game designer)


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Yellowjackets (band)

Yellowjackets is an American jazz fusion band founded in 1977 in Los Angeles, California.

History

In 1977, guitarist Robben Ford, for his first solo album, recruited keyboardist Russell Ferrante, electric bassist Jimmy Haslip and drummer Ricky Lawson. They decided to continue as a group and were signed to Warner Bros. Records by producer Tommy LiPuma, who chose the name "Yellowjackets" from a list of potential group names the band had compiled.

In 1984, the band's second album, Mirage a Trois, was nominated for a Grammy Award for Best Fusion Performance. Ford only played on half this album, and after he departed the group, saxophonist Marc Russo was hired in his place. The next album, Shades, reached No. 4 on the Billboard magazine jazz album chart, while the single "And You Know That" won a Grammy for Best R&B Instrumental Performance. Lawson left and was replaced by Will Kennedy in 1987. Their next three albums, Four Corners, Politics, and The Spin all received Grammy nominations for Best Jazz Fusion Performance. With Russo leaving the band in 1990, Bob Mintzer replaced him for the album Greenhouse, which reached No. 1 on the Billboard Contemporary Jazz Album chart. Mintzer has remained a band member.

The Yellowjackets celebrated their 30th anniversary in 2011 with the album Timeline for Mack Avenue. When Haslip took an extended hiatus, he was replaced by Felix Pastorius (son of bassist Jaco Pastorius.) The band released A Rise in the Road with Pastorius. On some of the songs, Pastorius played the fretless bass guitar made famous by his father.

In addition to their studio albums, the Yellowjackets contributed two tracks to the soundtrack of the film Star Trek IV: The Voyage Home in 1986.

Awards and honors
Grammy Awards
 * R&B Instrumental Performance: "And You Know That" (1987)
 * Jazz Fusion Performance: Politics (1989)

Grammy nominations
 * Jazz Fusion Performance: Mirage a Trois (1984), Four Corners (1987)
 * Contemporary Jazz Performance: Greenhouse (1992), Like a River (1994), Run for Your Life (1995), Dreamland (1996), Club Nocturne (1999)
 * Contemporary Jazz Album: Mint Jam (2003), Time Squared (2004), Lifecycle (2009)
 * Jazz Instrumental Performance: The Spin (1990)
 * Instrumental Composition: "Claire's Closet", Russell Ferrante (2009), "Civil War", Bob Mintzer (2014)
 * Best Large Jazz Ensemble Album: Jackets XL with the WDR Big Band (2022)

Current members

 * Russell Ferrante – keyboards, synthesizers (1977–present)
 * Bob Mintzer – saxophones, bass clarinet, EWI (1991–present)
 * William Kennedy – drums, percussion (1987–1999, 2010–present)
 * Dane Alderson – bass (2015–present)

Former members

 * Jimmy Haslip – bass (1977–2012)
 * Ricky Lawson – drums (1977–1987; died 2013)
 * Robben Ford – guitar (1977–1983)
 * Mike Miller – guitar (1983)
 * Michael Landau – guitar (1985)
 * Marc Russo – saxophones (1985–1989)
 * Peter Erskine – drums (1999–2000)
 * Terri Lyne Carrington – drums (2000)
 * Marcus Baylor – drums (2000–2010)
 * Felix Pastorius – bass (2012–2015)

Discography

 * 1981: Yellowjackets (Warner Bros.)
 * 1983: Mirage a Trois (Warner Bros.)
 * 1985: Samurai Samba (Warner Bros.)
 * 1986: Shades (GRP)
 * 1987: Four Corners (GRP)
 * 1988: Politics (MCA)
 * 1989: The Spin (MCA)
 * 1991: Greenhouse (MCA)
 * 1992: Live Wires (GRP)
 * 1993: Like a River (GRP)
 * 1994: Run for Your Life (GRP)
 * 1995: Dreamland (Warner Bros.)
 * 1995: Bobby McFerrin's Bang!Zoom (Blue Note)
 * 1997: Blue Hats (Warner Bros.)
 * 1998: Club Nocturne (Warner Bros.)
 * 2001: Mint Jam (Heads Up)
 * 2003: Time Squared (Heads Up)
 * 2003: Peace Round: A Christmas Celebration (Heads Up)
 * 2005: Altered State (Heads Up)
 * 2006: Twenty-Five (Heads Up)
 * 2008: Lifecycle (Heads Up)
 * 2011: Timeline (Mack Avenue)
 * 2013: A Rise in the Road (Mack Avenue)
 * 2016: Cohearence (Mack Avenue)
 * 2018: Raising Our Voice (Mack Avenue)
 * 2020: Jackets XL (Mack Avenue)
 * 2022: Parallel Motion (Mack Avenue)

title: Yellowjackets (band)


text:
User:Adhoert

What are you doing? Vandalism is not appreciated. RickK 00:42, 17 Nov 2003 (UTC)

title: User:Adhoert


text:
Zoombinis

Zoombinis was a series of educational puzzle computer games that were originally developed by TERC and published by Broderbund. In 1998, Broderbund was purchased by The Learning Company, (formerly SoftKey) who took responsibility for developing and publishing the series in 2001. The series consists of three games: Logical Journey of the Zoombinis (1996), Zoombinis: Mountain Rescue (2001), and Zoombinis: Island Odyssey (2002). Logical Journey was remade as Zoombinis for modern operating systems in 2015. The series focuses on the Zoombinis, small blue creatures each with different appearances and personalities, which the player must guide through strange puzzle-filled lands.

Logical Journey of the Zoombinis (1996)
Zoombini Isle, the Zoombinis' homeland, has been taken over by the evil Bloats. The Zoombinis flee but end up in a mysterious and treacherous land. Players must guide the Zoombinis through this land to reach the safety of Zoombiniville, a land of hope and prosperity for the Zoombinis. The original version of the game by Broderbund Europe in March 1996 came in English, French, and German. The US division of Broderbund made some minor changes and released a US version in December. As part of the US release they changed the names of several areas of the game.

Gameplay
The player starts at Zoombini Isle, where they assemble a team of 16 Zoombinis, picking from 5 different options each in hair, eyes, nose color, and footwear, for a total of 625 possible combinations. Each combination can be used twice in the game. The player then has to do a series of minigames, helping the Zoombinis traverse through dangerous places until they reach the next location on the island. By the end of a minigame, a number of Zoombinis may be left behind. At the end of a section, the Zoombinis can rest at a campsite and be stored to join another group of Zoombinis if there are fewer than 16 Zoombinis left. From the first campsite are two branching roads that take the Zoombinis to two different areas of the island and eventually join up at the second campsite before traversing to the final section of the island. At the end of the final section lies the target destination Zoombiniville. For each group of Zoombinis that make it through a section with all 16 in their group a monument is added to Zoombiniville. The game is won when 625 Zoombinis make it to Zoombiniville.

Zoombinis Logical Journey v2.0 (2001)
The US version of the original game was expanded and republished as Zoombinis Logical Journey v2.0 by The Learning Company in September 2001.

Zoombinis (2015)
In 2014, TERC began an internally funded redevelopment of Logical Journey of the Zoombinis. In February 2015, they launched a Kickstarter campaign to fund additional enhancements and releases and on 25 March, the campaign was funded successfully, with the total pledged double the original target of $50,000. The main improvements are updated graphics and the games ability to run on modern operating systems.

Zoombinis was officially released on 6 August 2015 for iPadOS, Android, Windows and MacOS, and for Fire OS on 28 October 2015 by TERC, FableVision, and Learning Games Network.

Zoombinis Mountain Rescue (2001)
After the foundation of Zoombiniville, the Zoombinis find peace once more, until a small group of them get trapped inside a cave seeking shelter from a storm. They meet up with strange creatures called Boolies who occupy a city known as Booliewood. As a result of the storm, the Boolies have been scattered across the land, and their mayor, the Grand Boolie Boolie, has disappeared. The goal of the game is to rescue a total of 400 Boolies and bring them to Booliewood to return the Grand Boolie Boolie.

Gameplay
The player begins in Zoombiniville, where they assemble a team of 16 Zoombinis. Like the previous game, the player has to get as many of the 16 Zoombinis through the minigames as possible, by making use of the Zoombinis' different characteristics in accordance to the patterns and principles of the minigames. Some of the minigames however require only the player's logic, regardless of the Zoombinis' characteristics. After all minigames are completed on a part of the land, the player progresses to play more minigames on the next part of the land. The gameplay takes more of an adventure game approach, as the number of Zoombinis on a part of the journey differ throughout different parts of the game after each checkpoint between Zoombiniville and Booliewood. The checkpoints are where Zoombinis that do not make it through minigames return to. The player also has the option to send the Zoombinis on different routes from checkpoints across the land to complete different minigames.

Zoombinis Island Odyssey (2002)
Long after the take over of Zoombini Isle at the hands of the Bloats, the island was completely stripped of its food and plant life, leaving the Zerbles and native moths hungry while the Bloats abandon the isle. A seagull travels to Zoombiniville and informs the Zoombinis of the situation. After an expedition of Zoombinis survey the damage on the island, they decide to bring caterpillars to restore balance to the island's chain of life.

Gameplay
The player begins by creating a group of 12 Zoombinis, which can be customized. The player must then complete different puzzles, such as growing berries and breeding moths, to eventually restore the ecosystem of the island. This game incorporates science concepts as well as math concepts into the puzzles, including intersection of rates, cryptography, astronomical time, Venn diagrams, and Punnett squares, as well as some reincarnations of puzzles from Logical Journey. The graphics have again received an update. The Zoombinis are fully 3-D, but their features no longer affect gameplay. When the Zoombinis release 224 Zerbles into the wild, the game is won.

Educational effects
As a computer game, Zoombinis is an entertaining activity for students from elementary to middle school. However, as an educational tool, Zoombinis stands above many other mathematical, analytical, and logical educational methods. The game works with problem solving through mathematics, deduction, and hypothesis testing primarily by clearly stating the goal of the problem at hand, with the option to either deduce for one's self or learn from with gameplay strategies for success. In 2015, the National Science Foundation awarded TERC nearly $2 million to study how much "computational thinking" kids do while playing Zoombinis (2015), both at home and in the classroom, and whether teachers can extend the lessons outside the game.

Mathematical aspects
The different games a player encounters when trying to get the Zoombinis from Zoombini Isle to Zoombiniville represent many mathematical characteristics. "Pizza Pass", "Allergic Cliffs", and "Stone Cold Caves" exercise the sorting, grouping, and comparing of information. "Captain Cajun's Ferryboat", "Stone Rise", and "Titanic Tattooed Toads" reinforce ordering, linking information, and problem solving. "Fleens!", "Mudball Wall", and "Hotel Dimensia" emphasize graphing and mapping, while "Lions' Lair", "Mirror Machine", and "Bubblewonder Abyss" train the player in sorting, organizing, and algebraic thinking.

Deductive reasoning
Sub-games such as "Allergic Cliffs" and "Stone Cold Caves" require the player to find patterns and arrangements of the Zoombinis in order to pass the obstacle. Each game also has a select number of attempts which may be failures before a Zoombini is taken back to the beginning of a path segment (to Zoombini Isle, or to the base camps of Shelter Rock and Shade Tree), giving an incentive for the player to think critically and not randomly guess answers. As a result, these games enable players' deductive skills while also enforcing strategic efficiency.

Hypothesis testing
Players also encounter critical thinking with testing and observing different logical outcomes in "Pizza Pass" and "Mudball Wall". By examining the varying characteristics of toppings on a pizza and the number and color of dots on a wall, the player can experiment with the correct patterns to get the Zoombinis to the next level. Similarly, with the deductive reasoning sub-games, these exercises discourage random guessing by giving only a few options to fail before losing a Zoombini. However, with the games that involve more hypothesis testing, the incorrect guesses remain on the screen in a categorized pile so that the player might learn from previous attempts to come to the correct conclusion.

Game effectiveness with students
With the game's release in the Spring of 1996, through its continued use in the present, observations of the game have shown it to be efficient and useful for students and teachers alike. As a learning tool, the game is fun and interactive for children born into the continuously evolving technological era of 2016. The characters are generalized, but still have a cartoonish look to entice any young person who wants to learn, and the format of the game inspires group work. The communication created between two or more players talking about how to find the right kind of pizza or nose, eyes, and hair matching Zoombini is a simple and effective way that students have fun learning with the game.

Awards

 * 2003
 * Zoombinis Island Odyssey
 * Bologna New Media Award
 * Won
 * }
 * }

title: Zoombinis


text:
Jump threading

In computing, jump threading is a compiler optimization of one jump directly to a second jump. If the second condition is a subset or inverse of the first, it can be eliminated, or threaded through the first jump. This is easily done in a single pass through the program, following acyclic chained jumps until the compiler arrives at a fixed point.

Benefits
The primary benefit of jump threading is the reduction of the amount of dynamically executed jumps. This makes way for further optimizations as there is a decrease in the number of conditionals, which will improve performance. On average one can expect 2-3 instructions being omitted as a result from a successful removal of a runtime branch.

Examples
The following pseudocode demonstrates when a jump may be threaded.

10. a = SomeNumber; 20. IF a > 10 GOTO 50 ...   50. IF a > 0 GOTO 100 ...

The jump on line 50 will always be taken if the jump on line 20 is taken. Therefore, for as long as line 100 is within the reachable range of the jump (or the size of the jump doesn't matter), the jump on line 20 may safely be modified to jump directly to line 100.

Another example shows jump threading of 2 partial overlap conditions:

The above can be transformed into:

If the first branch is taken,  and   are both true (logical conjunction), hence evaluation of expression   is not needed (logical disjunction). Therefore, a jump to label  is performed.

title: Jump threading