Greetings,
I’m wondering if it’s possible to control the output of a circle packing such that it produces a more “uniform” result. For example, I’ve noticed through some recent tinkering that this packing within a rectangle boundary, produced with a simple color gradient along the horizontal centerline (black in center fading to white at the upper and lower profiles) creates something that looks like it should, or could, have a more uniform and recognizable pattern - almost like a repeating sunflower. This is after an attempt at forcing the resultant mesh to have Tangent Incircles -
File below. Wondering if I’m on the right track, or if this is just wishful thinking? I suppose there are other ways of doing this that wouldn’t need the circles, and I’m interested in that as well. But my curiosity has more to do with the nature and control of circle packings.
Rectangular Circle Packing_00.gh (42.5 KB)
This image by Gyorgy Doczi gave me an idea, that maybe a conformal mapping from a logarithmic diagonal mesh from its circle boundary to a square could be interesting to try.
I thought it was interesting that relaxing the mesh gets the circles pretty close to tangent throughout. Adding the isothermic goal solves it for the centermost cells as well.
Happy with the symmetry after remapping to the square, but this is only a start. Would be nice to find a way to pack the seams and remove the obvious hole in the center in favor of something more distributed across a longer rectangle - closer to the image in the original post. The radii do matter - I’d like to be able to control the minimum and maximum, with the former being more important. Any ideas are welcome and appreciated!
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Nice Investigations. I have been at the “hollow” eye issue for ages myself, I think the best solution I have found was through Phyllotaxis, which is how them patterns present themeselves anyway, so maybe look into Phyllomachine and the Fibonacci sequence. In my experience all other directions are just rabbitholes leading into madness, I’ve been there, also in 3D 
Second best is building an incremental radial grid off a pentagon, ratio of triangles makes that initial “jump” less jarring. The simmetry that you display is lovely but a simplifying abstraction with its own limitations.
I hope this helps
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