Fibonacci Series
Robert P. Munafo, 2012 Dec 3.
The "Fibonacci series" is the series of muatoms R2.1/2a, R2.2/3a, R2.3/5a, R2.5/8a, and so on, where the numerator and denominator of the internal angle fraction are consecutive Fibonacci numbers F_{i} and F_{i+1}.
Because of mirror symmetry there are actually two Fibonacci series, the other being the series R2.1/2a, R2.1/3a, R2.2/5a, R2.3/8a, and so on, where the numerator and denominator are alternate Fibonacci numbers F_{i} and F_{i+2}.

In these pictures the filaments are very dense; every major branch point has 233 branches.
The "limits" of the two Fibonacci series are the internal angles 0.6180339887498... or 0.3819660112501... which are 1/Φ and 1/Φ^{2} where Φ is the Golden ratio.
revisions: 20121203 oldest on record
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 19872024.
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This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2012 Dec 05. s.27