### Neat Iterated Inversion Systems

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#### Ebanflo

• Fractal Friend
• Posts: 15

#### Neat Iterated Inversion Systems

« 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.

• 3f
• Posts: 1460

#### Re: Neat Iterated Inversion Systems

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

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
Fragmentarium is not a toy, it is a very versatile tool that can be used to make toys

https://en.wikibooks.org/wiki/Fractals/fragmentarium

#### Ebanflo

• Fractal Friend
• Posts: 15

#### Re: Neat Iterated Inversion Systems

« 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:

• 3f
• Posts: 1460

#### Re: Neat Iterated Inversion Systems

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

#### JoeEagar

• Fractal Freshman
• Posts: 4

#### Re: Neat Iterated Inversion Systems

« 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:

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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