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Primary Filament    

Robert P. Munafo, 2023 Mar 13.

A primary filament is part of a mu molecule but it not part of any smaller mu-unit. More accurately, (and for the R2 naming system) a primary filament is a maximal subset of a mu-molecule that does not intersect any of the mu-molecule's subset mu-units. This is a more restrictive definition than first order filament, which doesn't require the filament's owner to be a mu-molecule.

For example, compare the two figures in the mu-unit article. Figure 1 includes primary filaments; figure 2 approximates the appearance of the mu-unit R2.1/3 with the primary filaments removed.

Of all the islands in a primary filament, there is exactly one with lowest period. If that island is omitted, what remain are an infinite set of secondary filaments (see that article for examples). The filament subset operator (see R2 rules) gives names to the secondary filaments, and can be applied repeatedly to generate names for tertiary, etc. filaments.

See also primary filament operator.

revisions: 20020506 oldest on record; 20100918 add example; 20230313 add paragraph about secondary filaments

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2024.

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