Shorelines

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Offline pauldelbrot

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« Reply #75 on: February 21, 2020, 08:02:10 AM »
Fibonacci Bushes

Big bulb. Top bulb. Starfish bulb. Largest bulb between there and top bulb. Largest between there and starfish bulb. Largest ...

Keep on in that vein and you get ever bushier bushes like these, with arm counts that are the Fibonacci numbers. The sequence asymptotes to an irrational point on the cardioid boundary with internal angle the golden mean: the "classic" Siegel disk Julia set's parameter. You can see shapes resembling that Julia set's by setting the iteration limit deliberately too low in this Mandelbrot image, so that the interiors of the bushes become black.

Offline gerrit

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« Reply #76 on: February 21, 2020, 06:08:29 PM »
Nice. Which is "starfish bulb"?

Offline pauldelbrot

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« Reply #77 on: February 21, 2020, 09:31:26 PM »
The biggest one between the top (or bottom) bulb and seahorse valley. It has a five-armed starfish like shape attached to it.

Offline pauldelbrot

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« Reply #78 on: March 05, 2020, 01:00:52 AM »
Tangled Colorful Weeds

Offline pauldelbrot

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« Reply #79 on: March 17, 2020, 03:43:45 PM »
Bulb Four

Offline pauldelbrot

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« Reply #80 on: March 26, 2020, 07:49:05 AM »
Hairy Starfish

Offline pauldelbrot

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« Reply #81 on: April 08, 2020, 03:20:30 AM »
The Caramilk Secret

Offline pauldelbrot

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« Reply #82 on: April 17, 2020, 06:31:32 PM »
Cape of Storms

Offline pauldelbrot

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« Reply #83 on: April 27, 2020, 08:57:17 PM »
Swaddled

Offline pauldelbrot

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« Reply #84 on: May 08, 2020, 09:32:16 PM »
Polluted Shore

Offline pauldelbrot

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« Reply #85 on: May 22, 2020, 06:06:38 PM »
Mandelbrot Garden

Offline pauldelbrot

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« Reply #86 on: June 03, 2020, 09:16:09 AM »
Shapes in the Mist