Langford Chaotic Attractor

Langford Chaotic Attractor
Cindy Guzman
November 1st, 2021
George Mason University Math 401: Mathematics Through 3D Printing

For this past week, the main topic we analyzed and discusses was the various types of strange chaotic attractors. These attracts are made up of dynamical systems structured by ordinary differential equations (ODEs). ODEs explain the relationship between a function and its derivative (Meiss). What makes these systems chaotic consists of sensitive dependency and transitivity.

Out of the many strange chaotic attractors, I decided to print a Langford Chaotic attractor. This attractor was discovered from William F Langford. He wanted to come up with a model where he would produce toroidal chaos. His objective was to conduct research on bifurcations, when small changes are made to parameter values. The following ODEs were used:

dx/dt=(z-b)x-dy
dy/dt=dx+(z-b)y
dz/dt=c+az-z^3/3-(x^2+y^2)(1+ez)+fzx^3


Unfortunately, I wasn't able to print my object my