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A273485
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 742", based on the 5-celled von Neumann neighborhood.
1
4, 0, 12, -8, 20, -8, 44, -40, 52, -40, 76, -56, 84, -72, 156, -136, 164, -152, 204, -184, 212, -200, 284, -248, 308, -272, 364, -312, 452, -400, 588, -536, 484, -512, 668, -624, 612, -608, 700, -696, 692, -616, 668, -664, 884, -840, 1100, -1008, 1012, -960
OFFSET
0,1
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=742; 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}];
on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
Table[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)
CROSSREFS
Cf. A273482.
Sequence in context: A225952 A273795 A273858 * A151921 A273838 A273761
KEYWORD
sign,easy
AUTHOR
Robert Price, May 23 2016
STATUS
approved