• February 27, 2021, 01:48:57 PM

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Author Topic:  Period doubling in minibrots  (Read 973 times)

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Offline marcm200

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Re: Period doubling in minibrots
« Reply #15 on: February 08, 2021, 10:03:23 AM »
Is p the period of the biggest minibrot in the m/n wake ?
If yes then it's period is p = n+1

It looks that way. Image 1 below shows the area of period 20 (red), 21 (blue), 19 (green) and the red minibrot is a distorted one predicted from the yellow curve up to p19. The other minis from period 6 to 44 look the same.

What is the relation between
  • period p
  • internal angle m/n of main cardioid
and eccentricity ?
Is eccentricity proportional to p ?

In general, the eccentricity grows with increasing period, but not linearly, not even monotone. It looks from the first 40 periods as if they approach perhaps already a limit value (image 2).

As eccentricity here is calculated on the image pixel data and dependent on the numerically found periodic points to define the boundary of the cardioid, higher resolution and longer max it might give different values - and then, maybe, one gets a monotone relation. Here an image size of 4096 x 4096 and 25000 max it was used throughout.


Offline Adam Majewski

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Re: Period doubling in minibrots
« Reply #16 on: February 08, 2021, 09:35:01 PM »

Offline 3DickUlus

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Re: Period doubling in minibrots
« Reply #17 on: February 09, 2021, 06:13:24 AM »
Benford.


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