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.
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.
See also exploring.
revisions: 20000124 oldest on record; 20110228 add illustrations
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2012. Mu-ency index