Hénon map

Read more about the Hénon map at Wikipedia!

Here's the short version:

Start with x=0, y=0 and iterate

xn+1 = 1 + yn - 1.4xn2
yn+1 = 0.3xn


many many times and plot the points. They will appear like random dots to begin with but as they increase in number, magic happens. This is an illustration of the end result:

 

Hénon mapHénon map