http://code.activestate.com/recipes/tags/chaos/top/2015-10-16T19:52:02-07:00ActiveState Code Recipes2010-10-30T06:22:28-07:00FB36http://code.activestate.com/recipes/users/4172570/http://code.activestate.com/recipes/577445-dynamical-billiards-simulation/

<p style="color: grey"> Python recipe 577445 by <a href="/recipes/users/4172570/">FB36</a> (<a href="/recipes/tags/chaos/">chaos</a>, <a href="/recipes/tags/graphics/">graphics</a>, <a href="/recipes/tags/math/">math</a>, <a href="/recipes/tags/pil/">pil</a>, <a href="/recipes/tags/random/">random</a>). </p> <p>It simulates reflections of a ball on a billiards table that has one or more circular obstacles. (This can also be thought as a 2d ray-tracing.)</p> <p>Most of the time the path of the ball would be chaotic (meaning, if another ball started from any slightly different location or direction then its path would be very different after a short while). </p> <p>See Wikipedia for more info: <a href="http://en.wikipedia.org/wiki/Dynamical_billiards" rel="nofollow">http://en.wikipedia.org/wiki/Dynamical_billiards</a></p>

2015-10-16T19:52:02-07:00FB36http://code.activestate.com/recipes/users/4172570/http://code.activestate.com/recipes/579114-reaction-diffusion-simulation/

<p style="color: grey"> Python recipe 579114 by <a href="/recipes/users/4172570/">FB36</a> (<a href="/recipes/tags/chaos/">chaos</a>, <a href="/recipes/tags/fractal/">fractal</a>, <a href="/recipes/tags/graphics/">graphics</a>, <a href="/recipes/tags/image/">image</a>, <a href="/recipes/tags/images/">images</a>, <a href="/recipes/tags/math/">math</a>, <a href="/recipes/tags/mathematics/">mathematics</a>, <a href="/recipes/tags/physics/">physics</a>, <a href="/recipes/tags/simulation/">simulation</a>). Revision 2. </p> <p>Reaction-Diffusion Simulation using Gray-Scott Model.</p>

2013-06-20T06:57:57-07:00Steve Wadleyhttp://code.activestate.com/recipes/users/4186942/http://code.activestate.com/recipes/578572-dynamical-billiards-simulation/

<p style="color: grey"> Python recipe 578572 by <a href="/recipes/users/4186942/">Steve Wadley</a> (<a href="/recipes/tags/chaos/">chaos</a>, <a href="/recipes/tags/graphics/">graphics</a>, <a href="/recipes/tags/math/">math</a>, <a href="/recipes/tags/pil/">pil</a>, <a href="/recipes/tags/random/">random</a>). </p> <p>It simulates reflections of a ball on a billiards table that has one or more circular obstacles. (This can also be thought as a 2d ray-tracing.)</p> <p>Most of the time the path of the ball would be chaotic (meaning, if another ball started from any slightly different location or direction then its path would be very different after a short while). </p> <p>See Wikipedia for more info: <a href="http://en.wikipedia.org/wiki/Dynamical_billiards" rel="nofollow">http://en.wikipedia.org/wiki/Dynamical_billiards</a></p>

2013-04-29T14:35:53-07:00FB36http://code.activestate.com/recipes/users/4172570/http://code.activestate.com/recipes/577866-complex-polynomial-roots-fractal/

<p style="color: grey"> Python recipe 577866 by <a href="/recipes/users/4172570/">FB36</a> (<a href="/recipes/tags/chaos/">chaos</a>, <a href="/recipes/tags/fractal/">fractal</a>, <a href="/recipes/tags/math/">math</a>, <a href="/recipes/tags/mathematics/">mathematics</a>). Revision 2. </p> <p>The code generates complex polynomials that has random real coefficients; each +1 or -1. Later it plots the roots.</p> <p>Warning: The calculation may take 15 minutes or so!</p>

2011-08-14T23:09:08-07:00FB36http://code.activestate.com/recipes/users/4172570/http://code.activestate.com/recipes/577841-fuzzy-logic-fractal/

<p style="color: grey"> Python recipe 577841 by <a href="/recipes/users/4172570/">FB36</a> (<a href="/recipes/tags/chaos/">chaos</a>, <a href="/recipes/tags/fractal/">fractal</a>, <a href="/recipes/tags/math/">math</a>, <a href="/recipes/tags/mathematics/">mathematics</a>). </p> <p>This fractal created by converting logic statements into equations using fuzzy logic operators:</p> <p>X: X is as true as Y is true</p> <p>Y: Y is as true as X is false</p> <p>See: Scientific American Magazine, February 1993, "A Partly True Story"</p>

2011-08-02T03:53:03-07:00FB36http://code.activestate.com/recipes/users/4172570/http://code.activestate.com/recipes/577816-synchronized-chaos-using-lorenz-attractor/

<p style="color: grey"> Python recipe 577816 by <a href="/recipes/users/4172570/">FB36</a> (<a href="/recipes/tags/chaos/">chaos</a>, <a href="/recipes/tags/fractal/">fractal</a>, <a href="/recipes/tags/math/">math</a>, <a href="/recipes/tags/mathematics/">mathematics</a>). </p> <p>2 chaotic Lorenz dynamical systems get synchronized with time. (Notice 2 y and 2 z values start differently but approach each other later.)</p> <p>I used the x variable as the synchronization signal but y or z can also be used.</p>

2011-05-02T01:59:45-07:00FB36http://code.activestate.com/recipes/users/4172570/http://code.activestate.com/recipes/577681-spring-mass-system-simulation/

<p style="color: grey"> Python recipe 577681 by <a href="/recipes/users/4172570/">FB36</a> (<a href="/recipes/tags/chaos/">chaos</a>, <a href="/recipes/tags/math/">math</a>, <a href="/recipes/tags/mathematics/">mathematics</a>, <a href="/recipes/tags/physics/">physics</a>, <a href="/recipes/tags/simulation/">simulation</a>). </p> <p>It simulates a damped spring-mass system driven by sinusoidal force.</p>

2010-12-10T03:31:50-08:00FB36http://code.activestate.com/recipes/users/4172570/http://code.activestate.com/recipes/577487-chaotic-function-analysis-graph/

<p style="color: grey"> Python recipe 577487 by <a href="/recipes/users/4172570/">FB36</a> (<a href="/recipes/tags/chaos/">chaos</a>, <a href="/recipes/tags/graph/">graph</a>, <a href="/recipes/tags/graphics/">graphics</a>, <a href="/recipes/tags/math/">math</a>, <a href="/recipes/tags/mathematics/">mathematics</a>). Revision 2. </p> <p>There are 3 chaotic functions to graph as examples.</p> <p>Graph of function (0) is a curve. Graph of function (1) is a group of lines. (Both are Xn+1 = f(Xn) type functions.)</p> <p>Graph of function (2) on the other hand is a plane. (It is Xn+1 = f(Xn, Xn-1) type function.)</p> <p>These mean there is a simple relationship between the previous and next X values in (0) and (1). (Next X value can always be predicted from the previous X value by using the graph of the function w/o knowing the function itself.) But (2) does not have a discernible relationship. (No prediction possible!) So (2) is clearly more chaotic than others. (I think it could be used as a Pseudo-Random Number Generator (PRNG).)</p>

2010-12-07T09:54:51-08:00FB36http://code.activestate.com/recipes/users/4172570/http://code.activestate.com/recipes/577486-gumowski-mira-strange-attractor/

<p style="color: grey"> Python recipe 577486 by <a href="/recipes/users/4172570/">FB36</a> (<a href="/recipes/tags/chaos/">chaos</a>, <a href="/recipes/tags/fractal/">fractal</a>, <a href="/recipes/tags/math/">math</a>, <a href="/recipes/tags/mathematics/">mathematics</a>, <a href="/recipes/tags/pil/">pil</a>). Revision 4. </p> <p>It draws a random Gumowski-Mira Strange Attractor. (It would retry until a good one is found to display.)</p>

2010-11-16T06:00:51-08:00FB36http://code.activestate.com/recipes/users/4172570/http://code.activestate.com/recipes/577464-feigenbaum-constant-calculation/

<p style="color: grey"> Python recipe 577464 by <a href="/recipes/users/4172570/">FB36</a> (<a href="/recipes/tags/chaos/">chaos</a>, <a href="/recipes/tags/fractal/">fractal</a>, <a href="/recipes/tags/math/">math</a>, <a href="/recipes/tags/mathematics/">mathematics</a>). </p> <p>Feigenbaum constant calculation.</p> <p>For more info:</p> <p><a href="http://en.wikipedia.org/wiki/Feigenbaum_constant" rel="nofollow">http://en.wikipedia.org/wiki/Feigenbaum_constant</a></p>

2010-11-07T18:21:06-08:00FB36http://code.activestate.com/recipes/users/4172570/http://code.activestate.com/recipes/577455-dynamical-billiards-simulation-map/

<p style="color: grey"> Python recipe 577455 by <a href="/recipes/users/4172570/">FB36</a> (<a href="/recipes/tags/chaos/">chaos</a>, <a href="/recipes/tags/fractal/">fractal</a>, <a href="/recipes/tags/image/">image</a>, <a href="/recipes/tags/math/">math</a>, <a href="/recipes/tags/mathematics/">mathematics</a>, <a href="/recipes/tags/pil/">pil</a>). Revision 4. </p> <p>It creates fractal-like map plots from the simulation.</p> <p>(See my other post titled "Dynamical Billiards Simulation" first!)</p> <p>I had to keep image size and maxSteps small otherwise the calculation takes too long!</p> <p>(It shows what percentage of calculations completed every 10 seconds also.)</p>