Chaotic Attractors

Fernanda Garcia Camargo
MATH 401 - GMU Mathematics Through 3D Printing

Chaotic attractors are sets of states that a system can be in, but the exact state that the system will be in is unpredictable, even if we know the system's current state and the equations that govern it. This is because any small change in the initial state of the system can lead to a large difference in the system's state over time. Chaotic attractors are found in many different systems, including the weather, the stock market, and even the human heart. They are a fascinating example of how complex behavior can emerge from simple deterministic systems.

This week assignment is about The Lorenz Chaotic Attractor. It is a set of differential equations originally studied by Edward Lorenz in 1963. The Lorenz Attractor is a three-dimensional object whose body plan resembles a butterfly. The equations that describe the Lorenz system are:

dx/dt =σ(y−x)

dy/dt=x(ρ−z)−y

dz/dt=xy−βz

The most