There is also an ASCII version if this fractal animation here:
ASCII Julia Set Animation
Theory:
The shade of each individial pixel of the image is determined by how many
iterations it takes for the recursive equation z = z^2 +
c, for
c to have a
magnitude greater than or equal to 2, where
c and z are imaginary numbers.
Complex variable z is initialized as z = x + i*y, where x and y are the coordinates
of the pixel. The initial value of the complex variable
c is chosen
arbitrarily. In this animation, the real and imaginary parts of
c are
slowly interpolated as the animation runs.