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A279016
Binary representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 123", based on the 5-celled von Neumann neighborhood.
5
1, 10, 100, 1111, 100, 111011, 0, 11111111, 10000, 1110101111, 1000000, 111011111111, 1000000, 11111010111111, 100000000, 1111111111111111, 1010100000000, 111010101011111111, 101010000000000, 11101011111111111111, 10000010000000000, 1110111110101111111111, 10001000000000000, 111111101111111111111111, 100010101000000000000
OFFSET
0,2
COMMENTS
Initialized with a single black (ON) cell at stage zero.
Is this the same as A278916? - R. J. Mathar, Dec 05 2016
This sequence starts the same as A278916 but differs after a(23). - Robert Price, Dec 05 2016
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
MATHEMATICA
CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code = 123; 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[i, 2 * i - 1]], 10], {i, 1, stages - 1}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 03 2016
EXTENSIONS
Added a(24) to distinguish this sequence from A278916. - Robert Price, Dec 05 2016
Added a(22) and a(23) that were missing by Robert Price, Mar 02 2018
STATUS
approved