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, resulting in an infinite sphere packing.
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]
YouTube Encyclopedic
-
1/3Views:1 3741 3252 080
-
Geometry and arithmetic of sphere packings - Alex Kontorovich
-
T MAP Bonus Tutorial - Hexagon packing on a Sphere
-
Packing Spheres Efficiently and Learning how to Kiss in each Dimension - Dr. Stephanie Vance
Transcription
References
- ^ Borkovec, M.; De Paris, W.; Peikert, R. (1994), "The Fractal Dimension of the Apollonian Sphere Packing" (PDF), Fractals, vol. 2, no. 4, pp. 521–526, CiteSeerX 10.1.1.127.4067, doi:10.1142/S0218348X94000739, archived from the original (PDF) on 2016-05-06, retrieved 2008-09-15
- ^ ApolFrac
 | This fractal–related article is a stub. You can help Wikipedia by expanding it. |
 | This hyperbolic geometry-related article is a stub. You can help Wikipedia by expanding it. |
This page was last edited on 13 January 2024, at 09:47