File:Cml2e.gif

Summary
The animated gif demonstrates chaotic behavior in an uncoupled 2 dimensional lattice. Each site is updated by the logistic map $$ x_{n+1} = r x_n (1-x_n)$$. The range of the logistic map (randomly seeded between 0.1 and 0.5) is bounded from 0 to 1. The resulting animated contour map smooths the distinction between the sites with respect to the value they hold.

Each frame is taken at an iterative time step where the parameter r is increased $$ r=3.5,3.51,...,3.9 $$. Notably not until $$ 3.58 $$ does the map truly demonstrate chaotic behavior.