Neat Iterated Inversion Systems

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Offline Ebanflo

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« on: March 10, 2018, 09:29:07 PM »
I've been playing around with sets of 4 circles. For each point, if it is inside one of the circles, invert the circle. Count how many inversions it takes to be outside any of the 4 circles.

Linkback: https://fractalforums.org/share-a-fractal/22/neat-iterated-inversion-systems/1011/

Offline 3DickUlus

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« Reply #1 on: March 11, 2018, 12:37:44 AM »
I don't think I've seen this before, looks promising  :thumbs:

is the difference between the 2 images form different circle radii and positions?
are the circles uniform?

a pic of the circles used for each image would be great ;)

Offline Ebanflo

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« Reply #2 on: March 11, 2018, 02:30:29 AM »
For the first image the first circle is centered at (0,1) and has radius 1. The second circle is centered at about (1.4, 0.15) and has radius 2. The third circle is centered at (-2.6, 0.15) and has radius 2. The fourth circle is actually the infinite circle that is the lower half of the plane (so inversion is just reflection across the x-axis).

I'm not sure what the parameters for the second image were, because both images came from late-night messing around with this shader:
https://www.shadertoy.com/view/Xs2cDt

Offline 3DickUlus

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« Reply #3 on: March 11, 2018, 02:50:19 AM »
 O0 going to have to port that one to Fragmentarium ;)

Offline JoeEagar

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« Reply #4 on: April 08, 2018, 08:56:24 AM »
For the first image the first circle is centered at (0,1) and has radius 1. The second circle is centered at about (1.4, 0.15) and has radius 2. The third circle is centered at (-2.6, 0.15) and has radius 2. The fourth circle is actually the infinite circle that is the lower half of the plane (so inversion is just reflection across the x-axis).

I'm not sure what the parameters for the second image were, because both images came from late-night messing around with this shader:
https://www.shadertoy.com/view/Xs2cDt

Speaking of late-night messing around with Shadertoy shaders, I have found the parameters for the second image (or something close to it).  https://www.shadertoy.com/view/4sVyDG   That's an awesome fractal.


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