Julia Plot of the Complex Logistic Equation
This applet plots the Julia set for the complex logistic equation:
z(n+1) = k z(n)[1-z(n)], for k = 1.678 + .95 i. The equation is iterated
256 times for different starting values of z(n). If the equation is not
diverging to infinity at the end of the 256 iterations, then the starting point
z(0) is painted black. Hence the black area of the plot represents the Julia
set (except for some points on the outer corners that are also painted black
if they diverge on the first iteration). If, however, the equation begins
diverging (defined as occurring when the modulus of z(n+1) > 2), the iterations
are terminated, and the point is plotted with one of 16 colors. The iterations
cycle through this set of colors, but terminate when the equation diverges.
Hence, the color plotted indicates the rate the equation output is blowing
off to infinity.
The Java source code.