|
| |
|
|
A280614
|
|
Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 297", based on the 5-celled von Neumann neighborhood.
|
|
4
|
|
|
|
1, 0, 1, 12, 5, 50, 1, 244, 17, 964, 17, 4036, 85, 16170, 17, 65348, 277, 261194, 257, 1047676, 1281, 4190844, 69, 16774930, 5201, 67094820, 1, 268427228, 20561, 1073686308, 1, 4294932340, 87377, 17179650724, 21761, 68719291004, 267333, 274876975378, 344385
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,4
|
|
|
COMMENTS
|
Initialized with a single black (ON) cell at stage zero.
|
|
|
REFERENCES
|
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
|
|
|
LINKS
|
Robert Price, Table of n, a(n) for n = 0..126
Robert Price, Diagrams of first 20 stages
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
Wolfram Research, Wolfram Atlas of Simple Programs
Index entries for sequences related to cellular automata
Index to 2D 5-Neighbor Cellular Automata
Index to Elementary Cellular Automata
|
|
|
MATHEMATICA
|
CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code = 297; stages = 128;
rule = IntegerDigits[code, 2, 10];
g = 2 * stages + 1; (* Maximum size of grid *)
a = PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca = a;
ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k = (Length[ca[[1]]] + 1)/2;
ca = Table[Table[Part[ca[[n]] [[j]], Range[k + 1 - n, k - 1 + n]], {j, k + 1 - n, k - 1 + n}], {n, 1, k}];
Table[FromDigits[Part[ca[[i]] [[i]], Range[1, i]], 2], {i, 1, stages - 1}]
|
|
|
CROSSREFS
|
Cf. A280612, A280613, A280615.
Sequence in context: A299516 A278423 A278661 * A281041 A038331 A028578
Adjacent sequences: A280611 A280612 A280613 * A280615 A280616 A280617
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Robert Price, Jan 06 2017
|
|
|
STATUS
|
approved
|
| |
|
|
