Julia Set

This animation displays an example of the Julia Set. A brief introduction (along with a discussion of its relation to the Mandelbrot Set) can be found here.

The following formula is iterated, and if the value |z| exceeds 2, then it is assumed that it will go to infinity and does not belong to the set:
z_n+1=z_n²+c

Where
z=x+iy
c=a+ib

The Filled-In Julia Set consists of those initial values of z in the complex plane which do not diverge to infinity. To obtain the behavior shown, parameter b is held steady at 0.35, and parameter a varies incrementally between 0.35 and 0.4.