Robert P. Munafo, 2002 Nov 29.
A 4-dimensional space in which the Julia and Mandelbrot iterations are performed.
Two dimensions correspond to the Parameter values C used to start the Iteration; the other two dimensions correspond to the Z values.
Julia Sets are cross-sections in the Z plane. The Mandelbrot Set is a cross-section in the C plane passing through the origin.
If you are viewing an area of the Mandelbrot Set near a point P, then the most obvious features of the filaments in the area will resemble the Julia Set for C=P. Furthermore, the region near that point P in that Julia Set will resemble a region near P in the Mandelbrot Set, except for a scaling and rotation. This is the Main Diagonal Symmetry.
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2023. Mu-ency index
This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2002 Nov 30. s.27