Thomas Cyclically Symmetric Attractor

This was created at George Mason University for Math 493: Mathematics Through 3D Printing, taught by Dr. Evelyn Sander.

Provided here is a model of the Thomas Cyclically Symmetric Attractor, created in Mathematica using the equations

dx/dt=sin⁡y-bx
dy/dt=sin⁡z-by
dz/dt=sin⁡x-bz

using the parameter b = 0.1998 with initial conditions (1,0,1).

Discovered by Rene Thomas, the Thomas attractor is an example of a strange or chaotic attractor. Attractors are values for which a system of ODEs tend towards in the limit, i.e. they are stable equilibria. Strange attractors differ from attractors in that they are chaotic, meaning that slight changes in the initial conditions cause huge changes in the solutions.

Slight changes in this parameter b have drastic effects on the stability of the solutions to this ODE. This particular .thing file uses b = 0.1998 because it creates a very interesting geometry. For b > 1 we see a stable equilibrium, and for b = 1 we see the first bifurcat