http://code.activestate.com/recipes/tags/chaos-fractal/2013-06-20T06:57:57-07:00ActiveState Code Recipes2013-06-20T06:57:57-07:00Steve 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>

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>

2010-10-30T06:22:28-07:00FB36http://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>

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>