Alternative 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
terminal value z(n+1) = z(256) is assigned a color based on the value of the
square of its modulus (i.e., on the value of x2+y2).
Hence, the brightly colored area of the plot consists of the Julia set. If, however,
the equation begins diverging (defined as occurring when the modulus of
z(n+1) > 2), the iterations are terminated, and the point z(0) is painted black.
Hence the black area of the plot represents points that diverge and which are
therefore not in the Julia set.
The Java source code.