Robert P. Munafo, 2002 Apr 20.

Escape-Iterations = N(Max®) = Max(N)
(also called dwell) The value of N when R reaches a maximum. Because R is constrained by the escape radius, this ends up being equal to Max(N), the maximum value of N.

This is the traditional way of representing the Mandelbrot Set.

External-Angle = R(N(Max®)) = R(Max(N)
The value of R at the last iteration.

Atom-Domain-Period = N(Min®)
The value of N when R reaches a minimum. The initial value of R is ignored because it is zero.

This function yields an excellent way of locating mu-atoms of a given period. The image produced contains regions of solid color that surround the mu-atoms, because the minimum R value occurs when the number of iterations is equal to the period of the mu-atom. Each color corresponds to a different period value. All island mu-molecules, no matter how small, can be located easily by this method.

Distance-Estimator = ln(zz) z / dz
where z = Z(Max(N)), dz = iterated deriviative.

DEM-Dwell Hybrid
Plotting distance estimator and escape iterations at the same time, which is accomplished by using a two-dimensional mapping onto color space (see color).

Iterate Tracks or Buddhabrot
Plotting every Iterate value of Z during iteration of each point (like the plotting used with the Inverse-Iteration Method, except forward iterating using the Mandelbrot iteration, not the Julia Set iteration. See Buddhabrot for more about this plotting method.

See also Color.

Some unique functions (see below) have been suggested by Kerry Mitchell .

The Atom-Domains function is from Scott Huddleston .