• January 17, 2022, 04:34:51 PM

Author Topic: (Other) quaternion 3d mandelbrot with a twist  (Read 749 times)

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Offline haversin

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(Other) quaternion 3d mandelbrot with a twist
« on: October 08, 2021, 07:28:02 PM »


Linkback: https://fractalforums.org/index.php?topic=4443.0

Offline Tas_mania

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Re: quaternion 3d mandelbrot with a twist
« Reply #1 on: October 10, 2021, 09:53:33 AM »
This is pretty cool. I haven't done anything with quaternion because its kind of formless. But that's the beauty of it and your video shows that very well  :thumbs:

Offline haversin

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Re: quaternion 3d mandelbrot with a twist
« Reply #2 on: October 10, 2021, 04:28:57 PM »
Thanks, I just started experimenting with quaternions and I know they where tried early on for 3D fractals and got the reputation for being boring. But I'm having fun and who knows I might just find some “gold in them thar hills”

Offline marcm200

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Re: quaternion 3d mandelbrot with a twist
« Reply #3 on: October 10, 2021, 06:22:51 PM »
--- got the reputation for being boring.
There is an interesting map for the coquaternionic case with a slightly different algebra. When focusing on  the basins of attraction of one of the several cycles, there might be interesting structures to explore (fig. 3) in:

Code: [Select]
Falcao MI et al.
Basins of attraction for a quadratic coquaternionic map.
2017.
https://www.researchgate.net/publication/320768143_Basins_of_attraction_for_a_quadratic_coquaternionic_map

Offline haversin

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Re: quaternion 3d mandelbrot with a twist
« Reply #4 on: October 10, 2021, 08:46:46 PM »
Thanks for the reference. I did not know about coquaternions! j*j = k*k = i*j*k = 1 ?  :awe:


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