Apollonian sphere packing

Apollonian sphere packing is a way of arranging spheres (3D circles) so that they fill space efficiently. Starting with three mutually touching spheres, you can repeatedly place smaller spheres in the gaps between them. This process creates a complex arrangement of spheres, with each layer of spheres fitting snugly against the others. The result is a beautiful, intricate pattern that showcases both mathematical principles and geometric beauty. Apollonian sphere packing can be seen in nature, such as in the way some fruits cluster or in certain crystal structures.