A246310 Number of ON cells at generation n of 2-D cellular automaton in which a cell is ON iff either 1 or 4 of its eight neighbors were ON at previous generation, starting with a single ON cell.

1, 8, 8, 25, 4, 32, 32, 100, 25, 61, 88, 208, 112, 164, 232, 380, 188, 304, 341, 596, 437, 576, 528, 696, 553, 749, 736, 924, 1016, 1060, 1161, 1372, 1200, 1388, 1456, 1720, 1493, 1761, 1660, 2072, 1781, 2084, 1973, 2732, 2252, 2596, 2552, 3121, 2684, 3145, 2972, 3828, 3132, 3588, 3480, 4061, 3772, 4073, 4009, 4929, 4264, 4996, 4845, 5493, 5160, 5804, 5156

Offset: 0

Author

N. J. A. Sloane, Aug 23 2014

Keywords

• nonn
• look

Comments

This is the Rule 780 outer totalistic 8-neighbor 2-D CA.

The first few generations are easy to understand, but then there are complications (hence the keyword "look", which refers to the illustrations).

Links

• N. J. A. Sloane, Illustration of first 28 generations.
• N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168, 2015

Crossrefs

Cf. A253086 (5-celled analog).

Programs

Mathematica

Total@*Total /@ CellularAutomaton[{780, {2, {{2, 2, 2}, {2, 1, 2}, {2, 2, 2}}}, {1, 1}}, {{{1}}, 0}, 66]
ArrayPlot /@ CellularAutomaton[{780, {2, {{2, 2, 2}, {2, 1, 2}, {2, 2, 2}}}, {1, 1}}, {{{1}}, 0}, 28]