Chaotic Attractor

George Mason University Math 401: Mathematics Through 3D Printing
Nick Maranto
11/21/24

This week's project was about chaotic attractors. A chaotic attractor is a dynamical system that has an infinite number of periodic orbits. Also, when you make a small change in the initial condition in a chaotic attractor leads to large differences in the trajectory. When you take a cross section of a chaotic attractor, it is comprised of a Cantor set. In this project, I printed an attractor with two different parameter values.
The two 3D prints are Thomas attractors. A Thomas attractor is a dynamical system with the differential equations:
x’ = sin(y) – b*x
y’ = sin(z) – b*y
z’ = sin(x) – b*z.
The constant b is varied between the two prints. The print with chaotic trajectory has a b value at 0.2081 while the periodic trajectory has a b value at 0.19. Visually, the two prints are drastically different with such a small change in the parameter. This dynamical system models damping force.