Nested Mandelbrots

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Offline quadralienne

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« on: June 09, 2019, 06:33:21 PM »
Hi! I am new here but I have been exploring fractals for over 30 years ... and my first post here is something fun to watch ...

Suppose that instead of escaping from a circle of radius 2, z had to escape from another Mandelbrot set? ... and suppose that inner Mandelbrot set's z did too, recursively (forever, or at least until it's lost in the anti-aliasing :D )? We could colour the pixels based on some combination of arg(all-those-z-values) ... then just suppose those nested Mandelbrots were rotating, and we put another, darker version of this inside the first Mandelbrot and those ones are rotating in alternate directions so sometimes the rotations cancel out? Hey, maybe we're zooming out and transitioning the brightness a bit so it loops ... yeah, loop this video!

https://www.youtube.com/watch?v=_vw_DrxW1l4

I have more ideas than time to implement ... let me know what you think! I've got something on ShaderToy too!

Offline LionHeart

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« Reply #1 on: June 10, 2019, 02:58:25 AM »
Hi quadralienne,

This is rather cute. Well done. Please share more of your ideas with us.

Thanks.
Paul the LionHeart

Offline quadralienne

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« Reply #2 on: June 10, 2019, 02:06:25 PM »
One thing I find really neat is how the circles in even the deeply-nested Mandelbrot forms are still circular.

Offline quadralienne

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« Reply #3 on: June 10, 2019, 02:18:16 PM »
Also works well with connected Julia sets, but Mandelbrot is faster since I can check the main circle/cardioid before doing any recursion.

Offline quadralienne

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« Reply #4 on: June 10, 2019, 02:49:14 PM »
Also ... while the rainbow colouring can seem garish, it also makes it possible to animate the fractal with RGB LEDs! (The video can't do it justice :D )

https://www.youtube.com/watch?v=2t30rwP0YqY

Offline quadralienne

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« Reply #5 on: June 10, 2019, 02:50:48 PM »
aaand how about Magnet1M, with a different recursive fractal for each attractor? Still working on this one as it's quite CPU-intensive.

https://www.youtube.com/watch?v=KqNCxbgsLqM

Offline quadralienne

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« Reply #6 on: June 10, 2019, 02:52:13 PM »
one more thing for today -- be sure to loop this video too:

https://www.youtube.com/watch?v=XNBRG4m6A_I

Offline mrrudewords

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« Reply #7 on: June 10, 2019, 05:36:13 PM »
Super duper!
Z = Z2 + C (obvs)

Offline LionHeart

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« Reply #8 on: June 11, 2019, 03:42:41 AM »
Wowquadralienne,

These are really nice. Thanks for sharing them with us.

Offline Sabine62

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« Reply #9 on: June 11, 2019, 10:11:43 AM »
Thank you, quadralienne, great job!  :thumbs:
To thine own self be true

Offline quadralienne

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« Reply #10 on: June 12, 2019, 06:52:13 PM »
Glad y'all like it ... here's one from ShaderToy for those of you with nice GPUs: https://www.shadertoy.com/view/4tt3D2

... with some WIP //commented out  8)

Offline LionHeart

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« Reply #11 on: June 12, 2019, 11:25:22 PM »
Thanks quadralienne.

Nice. Keep 'em coming.

Offline quadralienne

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« Reply #12 on: June 13, 2019, 05:19:01 PM »
oddly this one is almost 15 years old!

Offline LionHeart

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« Reply #13 on: June 13, 2019, 11:07:26 PM »
Nice. Thanks for sharing it  :)


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