Apollonian sphere packing

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Apollonian sphere packing

Apollonian sphere packing is the three-dimensional equivalent of the Apollonian gasket. The principle of construction is very similar: with any four spheres that are cotangent to each other, it is then possible to construct two more spheres that are cotangent to four of them.

The fractal dimension is approximately 2.473946 (±1 in the last digit).[1]

Software for generating and visualization of the apollonian sphere packing: ApolFrac.[2]


  1. ^ Borkovec, M.; De Paris, W.; Peikert, R. (1994), "The Fractal Dimension of the Apollonian Sphere Packing" (PDF), Fractals, 2 (4), pp. 521–526, CiteSeerX, doi:10.1142/S0218348X94000739, archived from the original (PDF) on 2016-05-06, retrieved 2008-09-15
  2. ^ ApolFrac