Binary Decomposition
Robert P. Munafo, 1998 May 4.
A Representation Function which represents the Mandelbrot Set in a way that lends itself well to casual study of External Angle.
The Level Sets and Field Lines are superimposed, creating a sort of grid, and the "squares" of the grid are filled with N-digit binary numbers giving the first N binary digits of the external angles of field lines passing through the square. (Alternately, only the Nth binary digit is used.) Each level set is divided into 2n squares. It is easy to "read" the external arguments of points in the boundary of the Mandelbrot Set using a binary decomposition.
The simplest way to create a binary decomposition plot is to use the ordinary escape-iterations algorithm with a very large escape radius, and plot the Nth bit of the binary decomposition by noting whether the escaped value of Z (the Nth iteration) has a positive imaginary component.
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo. Mu-ency index
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