Boundary of the Mandelbrot Set  

Robert P. Munafo, 1999 Feb 3.



The boundary of the Mandelbrot Set contains all of the chaotic behavior in the iteration algorithm: all points that iterate indefinitely without a period are in the boundary. All "interesting" views of the Mandelbrot Set contain points in the boundary.

The boundary can be mapped one-to-one onto a circle (see external angle), but at the same time it is infinitely convoluted, having a Hausdorff dimension of 2.0.

The boundary of the Mandelbrot Set is a fractal by Mandelbrot's definition, but not by the simple "dimension" definition since its dimension is 2.0. The Mandelbrot Set itself (boundary plus interior) is not a fractal by any definition.

See also connected, interior.




From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2017.     Mu-ency index


Robert Munafo's home pages on HostMDS   © 1996-2017 Robert P. Munafo.
aboutcontact    mrob    mrob27    @mrob_27    mrob27
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Details here.

This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2017 Feb 02. s.11