Combining strange with strange...........I remember what I read in a book on fractal patterns...........and chaos theory..........in a book in MLK library here in DC..............kinda like a cartoon, compacted version.............it mentioned Julia sets..........the M. set...........and F. constant...............it said if u overlapped period two cascading and the M. set............u would have a key to "untold mysteries".............yep, pretty much..........I am not making this up................it is a pattern...........




What is even stranger..................4, 6................the 1st two non primes in the pf......................6 * 4 = 24.................which is what the log of 3.1 predicts for the number of primes..............F's constant begins...................4.6....................................



[PDF]Fibonacci order in the period-doubling cascade to chaos - CiteSeerX

citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.497.194&rep=rep1...pdf

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by G Linage - ‎2006 - ‎Cited by 20 - ‎Related articles

Diverse physical, chemical, and biological systems that dis- play the period-doubling route to chaos satisfy the scaling rela- tions predicted by the Feigenbaum constants δ and α [3]. ... These α scalings are pre- served for the higher-order periodic bifurcations throughout the period-doubling cascade.

Feigenbaum constants - Wikipedia

https://en.wikipedia.org/wiki/Feigenbaum_constants

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In mathematics, specifically bifurcation theory, the Feigenbaum constants are two mathematical constants which both express ratios in a bifurcation diagram for a non-linear map. They are named after the mathematician Mitchell Feigenbaum.

‎The first constant · ‎The second constant · ‎Properties

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The route to chaos - Farside.ph.utexas.edu.

farside.ph.utexas.edu/teaching/329/lectures/node55.html

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then the attractor undergoes a period-doubling bifurcation which converts it ... 2 offers reasonably convincing evidence that this ratio takes the constant value $F=4.69$ ... motion at various stages on the period-doubling cascade discussed above. ... Around 1975, the physicist Mitchell Feigenbaum was investigating a simple ...