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A278789
Decimal 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 78", based on the 5-celled von Neumann neighborhood.
4
1, 3, 3, 7, 11, 23, 43, 71, 219, 263, 795, 1863, 2267, 7047, 8603, 26567, 45275, 78471, 261531, 262343, 787419, 1313927, 2371483, 7639495, 9434331, 27264647, 56628635, 73427143, 232868827, 409269383, 968296347, 1325472199, 3808914651, 6125313671, 10123609499
OFFSET
0,2
COMMENTS
Initialized with a single black (ON) cell at stage zero.
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=78; 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]], 2], {i, 1, stages-1}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Nov 28 2016
STATUS
approved