#
The Quartic Map

## How to use this applet

In this applet you see on the right the analogue of the Mandelbrot set
i.e., the parameter plane for
the complex function **c z**^{2} (2 - z^{2}) 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 orbit of the free critical
point (at +1 or -1) is bounded while colored
points represent **c**-values for which the corresponding orbit of the
free critical point
escapes (with the same coloring scheme as above).

This applet was created by Yakov
Shapiro for Professor Robert
Devaney.