http://code.activestate.com/recipes/tags/chaos-random/2015-10-16T19:52:02-07:00ActiveState Code Recipes2015-10-16T19:52:02-07:00FB36http://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>

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>

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>

2011-08-02T03:53:03-07:00FB36http://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>

2011-08-14T23:09:08-07:00FB36http://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>

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>

2010-12-07T09:54:51-08:00FB36http://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>

2010-12-10T03:31:50-08:00FB36http://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>

2010-11-07T18:21:06-08:00FB36http://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>