Robert P. Munafo, 1996 Feb 8.

-1.6690 + 0.0029 i  +0.75
-1.6690 + 0.0029 i @ +0.75

-, , .)` -*_,. -b _@),c-de. ' . -, .'^@"F*^* '`,, ., 'b . ^ac.^d^ .____________e______L""`e_____a____\________a_a_ev_d__)aF"^` ` -"-r` ' `% '` ' ' ^^ -` "`@v-[ .` ' '" a~`.-*m-_ ' _arFrF$@Y .:F\ `:$` _/d` " .,*- '

R2-Name: R2F(1/2B)
Abbrev: RF(2B)
Colloq.: Spike, main antenna, proboscis
Coords: -1.6690 +0.0029i @ +0.7500

R2F(1/2B) is the R2-Name of the filament that lies on the real axis. It is the largest and most prominent filament, and thus has many colloquial nicknames.

It contains the largest island mu-molecule, R2F(1/2B1)S

The real axis itself, or specifically the line segment from -2.0 to the Feigenbaum Point, comprises a significant portion of R2F(1/2B). A large part of this line segment belongs to mu-molecules, but when these points are removed the result is a Cantor-like set that has positive measure (i.e. it has a non-zero total length).

David Doff has approximated the total length of this chaotic portion of the real axis, by using the method to measure pixels on a line which approaches the real axis asymptotically from above. The grid density and iterations are increased at the same time. The result is 0.55.


Measure of chaotic region: David Doff, Trinity College, Dublin

revisions: 19960208 oldest on record; 20120126 add picture

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

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