Symmetric Chaos
The applet above iterates the map of the complex plane defined by
z' = (az+b |z|2 z + c (z*)n-1) exp(-d*|z|2)
where z* is the complex conjugate of z, and a,b,c and d are
real parameters. The quantity n gives the order of the symmetry (that
of a regular n-gon) and must be an integer. The dark green region
shows the square [-2.5,2.5]2 in the complex z-plane. Iterates
are plotted 1000 at a time.
- Choose initial conditions with the left mouse button; a random colour will
be selected for each new initial condition.
- Clear the trajectories shown or continue by using the buttons at the top.
- Edit the parameter values to see a variety of different symmetric
(but chaotic) attractors.
Have fun!
P.Ashwin@ex.ac.uk
Updated 14th March 2001