Chaotic Attractor

Exploring Chaotic Attractors via 3D printing
Dylan Evans
November 23 2024
George Mason University Math 401: Mathematics Through 3D printing

Chaotic attractors are mathematical structures that exhibit unpredictable behavior while remaining bounded within a region of space. The study of such structures connects fields of nonlinear dynamics, differential equations, and geometry offering a theoretical and applied point of view. For this project, I created an attractor that starts off as two separate spirals that, while the parameters increase, combines the spirals into one larger spiral much like two colliding galaxies. The attractor is defined by three differential equations with three parameters controlling the dynamics of the system. Using Mathematica, I numerically solved the system and visualized the data converting it into a 3D printable model in the end.

First I created the differential equations, F1(x,y,z):= a(y-x), F2(x,y,z):= x(b-z)-y and F3(x,y,z):= xy-cz where the coupled ter