File:Cml2e.gif

Template:Information

The animated gif demonstrates chaotic behavior in an uncoupled 2 dimensional lattice. Each site is updated by the logistic map ${\displaystyle x_{n+1}=r{x}_n(1-x_n)}$. 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 ${\displaystyle r=3.5,3.51,...,3.9}$. Notably not until ${\displaystyle 3.58}$ does the map truly demonstrate chaotic behavior.

Template:Self

Template:Copy to Wikimedia Commons