Filament

Robert P. Munafo, 2011 Feb 28.

Any contiguous subset of the Mandelbrot Set which consists of the infinitely convoluted and branching structures that connect the island mu-molecules to each other.

Some figures from the delta Hausdorff dimension article. All of the black features consist of filaments. Interior and non-member points are white.

The filaments contain all the variety in the Mandelbrot Set. While the islands are extremely alike, the filaments attached to them are remarkably different. Any two filaments which appear alike actually contain many subtle differences.

Some of the most remarkable subtle differences in filaments are to be seen when investigating embedded Julia sets.

Some colloquial names for filaments: antenna, main antenna, spike, spoke.

See also exploring.

revisions: 20000124 oldest on record; 20110228 add illustrations

Mu-ency main page — index — recent changes — DEMZ

This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2011 Dec 08.

s.27