Fibonacci and fractals

[pascal2]

Hi folks.  Apparently the Mandelbrot set contains Fibonacci numbers featurally- see https://www.google.com/search?q=fibonacci+sequence+mandelbrot+set&sxsrf=ALiCzsb_irvWQNtwqTG9a3p4iNQUe_mEuQ%3A1665703056265&source=hp&ei=kJxIY-SiC4qgptQPruqYoAI&iflsig=AJiK0e8AAAAAY0iqoBFE2gcFb2WtNBdbrLa5X-qlKlMe&oq=f&gs_lcp=Cgdnd3Mtd2l6EAEYADIECCMQJzIECCMQJzIECCMQJzIFCAAQkQIyCwgAEIAEELEDEIMBMgUIABCRAjILCAAQgAQQsQMQgwEyBQgAEIAEMgsIABCABBCxAxCDATIRCC4QgAQQsQMQgwEQxwEQ0QNQAFgAYIIjaABwAHgAgAFYiAFYkgEBMZgBAKABAQ&sclient=gws-wiz#kpvalbx=_l5xIY--DKu-u5NoPlviH6Ao_31

 

Does anyone know if other 'Generalized' Fibonacci numbers are present featurally in similar fractal figures? Or even more general patterns such as those presented by Metallic Means, Pisot-Vijayarhagavan numbers, etc.? Thanks.

[Vmedvil5]

50 minutes ago, pascal2 said:

Hi folks.  Apparently the Mandelbrot set contains Fibonacci numbers featurally- see https://www.google.com/search?q=fibonacci+sequence+mandelbrot+set&sxsrf=ALiCzsb_irvWQNtwqTG9a3p4iNQUe_mEuQ%3A1665703056265&source=hp&ei=kJxIY-SiC4qgptQPruqYoAI&iflsig=AJiK0e8AAAAAY0iqoBFE2gcFb2WtNBdbrLa5X-qlKlMe&oq=f&gs_lcp=Cgdnd3Mtd2l6EAEYADIECCMQJzIECCMQJzIECCMQJzIFCAAQkQIyCwgAEIAEELEDEIMBMgUIABCRAjILCAAQgAQQsQMQgwEyBQgAEIAEMgsIABCABBCxAxCDATIRCC4QgAQQsQMQgwEQxwEQ0QNQAFgAYIIjaABwAHgAgAFYiAFYkgEBMZgBAKABAQ&sclient=gws-wiz#kpvalbx=_l5xIY--DKu-u5NoPlviH6Ao_31

 

Does anyone know if other 'Generalized' Fibonacci numbers are present featurally in similar fractal figures? Or even more general patterns such as those presented by Metallic Means, Pisot-Vijayarhagavan numbers, etc.? Thanks.

Very Interesting Pascal, and I don't know the answer to your question, sorry. Maybe Superpolymath aka JeffreyTubes would know he nerds out on those fractal patterns.

Edited October 14, 2022 by Vmedvil5