Rucklidge Attractor

Taylor Fountain
MATH 401 - Math with 3D Printing
George Mason University

A strange attractor is an attractor of a dynamical system (ie. the set of values that a dynamical system tends towards) that takes on a fractal structure, which is usually indicative of the system being chaotic. A chaotic system is a dynamical system that exhibits sensitive dependance on initial conditions, and it's attractors can be subclassed as chaotic attractors: sets of values that towards which the system exhibits global stability, despite it's arbitrary pieces exhibiting instability. One such strange attractor is the Rucklidge model, which is the dynamical system described by the set of equations:

dx/dt = -kx+ly-yz
dy/dt = x
dz/dt = -z+y^2

This system exhibits chaotic behavior where k=2 and l=6.7, with initial conditions (x0,y0,z0) = (1, 0, 4.5).

To construct a 3D object of this system, I input the system into Mathematica (see attached file), evaluated the system with the initial conditions