A351784 Number of cells containing one or more grains of sand after n grains of sand are added to one cell in an initially empty and infinite 3D cubic grid for the 3D sandpile model.

0, 1, 1, 1, 1, 1, 6, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 7, 6, 7, 7, 7, 7, 7, 24, 25, 25, 25, 25, 25, 24, 25, 25, 25, 25, 25, 24, 25, 25, 25, 25, 25, 24, 25, 25, 25, 25, 25, 24, 25, 25, 25, 25, 25, 24, 25, 25, 25, 25, 25, 24, 25, 25, 25, 25, 25, 24, 25, 25

Offset: 0

Author

Scott R. Shannon and Zach J. Shannon, Feb 19 2022

Keywords

• nonn

Comments

The 3D sandpile model follows the same rules as the 2D model except that cells topple and transfer one grain of sand to their six nearest neighbors when the cell contains 6 or more grains. Cells containing 0 to 5 grains are stable.

Links

• Scott R. Shannon, Table of n, a(n) for n = 0..10000
• Per Bak, Chao Tang, and Kurt Wiesenfeld, Self-organized criticality: An explanation of the 1/f noise, Phys. Rev. Lett. 59 (1987), 381-384.
• Laura Florescu, Daniela Morar, David Perkinson, Nicholas Salter, and Tianyuan Xu, Sandpiles and Dominos, Electronic Journal of Combinatorics, Volume 22(1), 2015.
• Luis David Garcia-Puente and Brady Haran, Sandpiles, Numberphile video, YouTube.com, Jan. 13, 2017.
• Zach J. Shannon, Image of the occupied cells for a(96)=44, bisected along the y-z plane. The colors are red=1 (24 total cells), blue=3 (14 total cells), violet=5 (6 total cells) grains per cell.

Crossrefs

Cf. A351783, A351379, A349990 (2D version), A307652, A259013, A180230.