After showing a first version of osculatory sphere packings in 
BaldEagle's "Pappus Chain" thread, I couldn't let the topic rest.

https://news.povray.org/povray.advanced-users/message/%3C66a14899%40news.povray.org%3E/#%3C66a14899%40news.povray.org%3E

In the image mentioned above, I cancelled the process after nine 
iteration steps in each packing. In the examples shown here, I have 
ended the process after 13 ‘generations’, which exhausts the 
possibilities of POV on my machine (Core I9 with 32GB RAM). Each of the 
following sphere packings consists of a total of 16,099,560 individual 
balls. With 14 generations one reaches a total of 54,118,529 spheres, 
which is beyond the capabilities of my machine.
In these pictures I have always used the initial configuration with the 
curvatures 1,2,2,3,3 (i.e. the radii 1,1/2,1/2,1/3,1/3), which all 
authors seem to agree on calling ‘apollonian’.
Even though the CGSphere competition was shut down in 2018, I used the 
scenario demanded there back then. The first image shows the Apollonian 
sphere packing in front of this classic CGSphere background with the 
material from the first image mentioned above: It still looks quite nice 
here, but in my eyes looks better in the first image.

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