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.