450:. I offset the restricted area to the right (the beige 'a', color chosen so that it wouldn't be anywhere else on the screen), and instead of just black dots, I used a spectrum as a heat-map. White areas were never visited, blue areas were visited very rarely, and red more frequently. Note that you can see the ghost of an additional pattern of the large A mirrored in position (but not mirrored in orientation) to the left of the image, and similar repetitions at each of the smaller scales as well. I suppose I should explain the exact algorithm for clarity. What I did was pick a corner at random, and jump 1/2 of the way to that corner from the current position. But if that new location would end up on the beige restricted area, it goes back to where it was and picks a different corner until it doesn't. This can be combined with other rule-sets for other effects, producing similar omitted areas, but also some inverted areas in other parts, some of which came out similar to your Q example linked above.
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misleading about that particular image - specifically, it appears to be inverted. Whereas all the other images on this page feature black dots being drawn on a white background, this one seems to have been done with white dots on a black background. i.e. the black areas on the image are those which were never visited, rather than those which were. I don't know if the image would be easier to understand if it were inverted, but it would be more consistent with the other images on the page.
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I had the same interrogation, so I looked up in
Wolfram and tried to clarify it : the thing is you choose a point at random inside the triangle only for the first point. Then you keep reusing your result as the initial point, switching vertices at random. You have to throw out the first few points,
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I fail to see how the chaos game could possibly generate the sierpinski triangle. If the criteria for plotting points is that they simply lie on the midpoint between any point inside the initial polygon (triangle) and one of the verticies of the initial polygon, then it's pretty easy to demonstrate
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So I've been doing a bit of experimentation with this, and the image showing the jump being restricted from landing on a particular area and causing a copy of that area to be seen at smaller scales around the field. (The one with the "Om" symbol.) Unless I'm missing something, there's something
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While it seems that particular one above has been clarified, this other description is particularly ambiguous. "A point inside a square repeatedly jumps half of the distance towards a randomly chosen vertex, but the currently chosen vertex cannot be 1 or 3 places, respectively away from the two
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Many of the descriptions of the images in the section on the restricted chaos game are unclear. On the second image for example ("the current vertex cannot be one place away from the previously chosen vertex"), the explanation is clearly false, as the current wording means that a random pair of
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i think these paragraphs should be reversed. the primary definition of "chaos game" is the general one, the polygon is an older meaning and a special case. furthermore it would be great to have an series of images illustrating how the attractor emerges as the samples generated by the game
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Same here! Wish someone can clarify that issue with "A point inside a square repeatedly jumps half of the distance towards a randomly chosen vertex, but the currently chosen vertex cannot be 1 or 3 places, respectively away from the two previously chosen vertices."
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It's been a little while but if I recall correctly, that one is essential "If the last two chosen vertices are the same, the next vertex can't neighbor that vertex". Here's the program that generated my version of the image:
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I just confirmed with code that Haas's description works for the pentagonal one as well. Only when the last two chosen vertices are the same do you not allow using their neighbors for the next chosen vertex.
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that all points inside the polygon will be plotted with almost equal probability. What am I not understanding about the chaos game?
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I think it's worth sharing my best attempt to replicate the effect of the chaos game with the Om symbol, found
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previously chosen vertices." I've tried to reproduce the image from the description but have been unable to.
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problem: the sierpinski gasket image shown was made with an L-system, not with the chaos game as claimed.
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antipodal vertices would be chosen and alternated between. Hopefully someone can clarify this.
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I'm puzzled when I try to re-construct what I did, but the Basic program I used is here:
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I never gave much attention to this code, but maybe it could be useful to someone.
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accumulate. and lay out the algorithm in step by step pseudo-code.
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