Apollonian Gasket

After a discussion on circle tangent to circles, I just wanted to look at Apollonian Gasket. I made little components based on Rhinocommon tools to find a circle tangent to 3 curves. Sometime circle is missing or I didn’t help enough the Rhino tool or tolerance is not good.

Some rendering using Möbius Transformation or not and a Recursive Circle Transform.

After Mobius Transform


Recreating Integral Apolloniancircle



ApollonianGAsket2CirclesRecursion.gh (15.0 KB)
IntegralApollonianPacking.gh (11.9 KB)

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i wish one day i am only half as capable as you are!

Thanks, here there is nothing really new. I reuse the logic described here. I added some limitation on radius and some parallel computing

What I am happy with is the Recursive Circle Transform. The idea is to use the biggest circle as reference (the plane or center for the orientation position and the radius for the size). Then apply some recursion.
This could lead to some fun shapes, in 2D or 3D
Begin with 4 circles (not on the sample plane here)


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Ahhh. Sweet man-made spherical tardigrade horrors beyond my comprehension…

I only wish I could even begin to understand how you achieve these things. : )

continues clicking icons in Rhino like a gorilla