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Fibonacci Series    

Robert P. Munafo, 2012 Dec 3.

The "Fibonacci series" is the series of mu-atoms 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 Fi and Fi+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 Fi and Fi+2.

-0.3906126 - 0.5868063 i @ 0.0001042
The area around R2.144/233a

The same area rendered with period domains up to period 2000.

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/Φ2 where Φ is the Golden ratio.

revisions: 20121203 oldest on record

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

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