First Order Filament

Robert P. Munafo, 2002 May 6.

A filament which is part of a given mu-unit and not part of any smaller mu-unit. Opposed to primary filament, which references filaments in relation to mu-molecules.

For example, look at the figures under the entries R2.1/3 and R2F(1/3B*). In both figures, the branch to the upper-left is a primary filament of the Mandelbrot Set. It is also a first order filament of the Mandelbrot set.

The branch on the bottom, however is not a primary filament of anything because it is part of the smaller mu-unit R2.1/3, and R2.1/3 is not a mu-molecule. However the bottom branch is made up of first order filaments. The upper portion of it is a first order filament of R2.1/3, and the rest is first order filaments of R2.1/3.1/2, R2.1/3.1/2.1/2, etc. See the mu-unit heading for an illustration of what is meant by "the mu-unit R2.1/3".


From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo.     Mu-ency index

Creative Commons License This work is licensed under a Creative Commons Attribution 2.5 License .
WWW: http://www.mrob.com/
EMail: mrob at mrob com (If you aren't a spambot you can rewrite this yourself)
© 1996-2008 Robert P. Munafo.s.13