In this applet you see on the right the analogue of the Mandelbrot set i.e., the parameter plane for the complex function c z2 (2 - z2) where c is a complex parameter, and, on the left, the corresponding (filled) Julia set for the particular chosen c-value. The filled Julia set is displayed in black; the Julia set is the boundary of the black region. The colored points are the points whose orbits escape to infinity, with red points escaping fastest, followed by orange, yellow, green, blue, indigo, and violet. In the parameter plane, the black points represent c-values for which the critical orbit is bounded, while colored points represent c-values for which the corresponding orbit of 0 escapes (with the same coloring scheme as above).
This applet was created by Yakov Shapiro for Professor Robert Devaney.