# R2F(1/2B)

Robert P. Munafo, 1996 Feb 8.

*-1.6690 + 0.0029 i @ +0.75*

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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 Pixel Counting 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.

Acknowledgements

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) 1987-2022. Mu-ency index

This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2022 Mar 28. s.27