login
A271542
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 382", based on the 5-celled von Neumann neighborhood.
1
4, 7, 9, 16, 3, 36, -11, 59, -12, 73, -33, 85, -20, 139, -111, 164, -9, 97, -104, 207, 20, 44, -63, 200, 71, 57, -200, 319, 77, 96, -161, 265, 176, -25, -163, 331, 281, -188, -45, 409, 164, -173, 4, 332, 333, -212, -9, 225, 680, -693, 313, 388, 271, -435
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=382; 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. A271539.
Sequence in context: A370523 A024797 A271253 * A010424 A044903 A359016
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 09 2016
STATUS
approved