Great Software for Dynamical Systems

By Xah Lee. Date: . Last updated: .

StdMap

stdMap screenshot
StdMap http://amath.colorado.edu/faculty/jdm/programs.html Mac OS X

StdMap. Standard Maps displays the dynamics of several area preserving mappings. It will also find periodic orbits, cantori, and stable and unstable manifolds of any (symmetric) periodic orbit.

The program is written by mathematician J D Meiss.

1DMap

1DMaps icon
1DMap http://amath.colorado.edu/faculty/jdm/1DMaps.html Mac OS X

1DMap is another program by mathematician J D Meiss. It plots orbit maps of various equations, including: logistic, cosine, cubic, exp, tangent, tent, circle. For each, one can plot the correspondig cobweb, bifurcation diagram, and other statstical diagrams. The program is intuitive, but there is no documentation or tutorial, so the reader must already be familiar with the mathematics. Some text books on 1D dynamic systems are suggested on his website.

by mathematician J D Meiss.

Cycle Explorer

cycle explorer
cycle explorer

Cycle Explorer is a simple program that draws orbit maps of the equation f[x]:=x^2+c. Author is Jim Burgess.

http://www.efn.org/~jcburg/software.shtml Mac OS Classic (2003-10)

ABC Map

ABC Map screenshot
ABC Map

ABC Map “abc, iterate a 3D volume preserving system”. It plots orbit maps of what seems various 3D formulas of significance. I don't quite understand the math here. However, this program is wonderful in that it is like a screensaver with mesmeric images. Dots appears in a 3D box, and these dots fluctuate seemingly ramdomly that forms very distinct patterns. It's like watching statics on TV, but the statics form unpredicable patterns constantly. One can rotate the box. It is a fantastic program even if one knows nothing about the math. The equation it plots has these names: Froeshle, Arnold, ABC, Integrable, Adriana, and others. I hope the author writes a minimum amount of tutorial to benefit the masses.

by mathematician J D Meiss

http://amath.colorado.edu/faculty/jdm/abc.html Mac OS X (2003-10)

IFS

IFS screenshot
A pattern generated by J D Meiss's IFS

IFS Another program by mathematician J D Meiss. This program does the Iterated Function Systems. It comes with a tutorial on IFS. Nice. After reading the one-page tutorial, I understand that IFS is as follows: we have n mappings of the plane. For each iteration, one of them is chosen by a given probability function. So, we start with some points or line in a plane, then apply the functions in each iteration, and plot the transformed points or line accumulatively.

http://amath.colorado.edu/faculty/jdm/ifs.html Mac OS Classic (2003-10, 2012)

Icon Maker

icon maker screenshot
Icon Maker by Jim Burgess

Icon Maker is a simple program that draws orbit maps of the equation

f[z]:=z*(λ + α*z*conjugate[z]+β*Real[z^n]+ω*i)+γ*Conjugate[z]^(n-1)

and other variants. The program is based on ideas in the book Symmetry in Chaos by M Field, M Golubitsky, 1992. This is a wonderful, easy to use, and beautiful program. Author is Jim Burgess.

http://www.efn.org/~jcburg/software.shtml Mac OS Classic (2003-10)

Further Reading

[Non-liner science Frequently Asked Questions By James D Meiss. At http://amath.colorado.edu/faculty/jdm/faq-Contents.html ]

If you have a question, put $5 at patreon and message me.