# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a285781 Showing 1-1 of 1 %I A285781 #7 Apr 26 2017 22:57:01 %S A285781 1,10,10,0,1100,0,11000,0,11110000,0,1100000,0,100111000000,0, %T A285781 1100110000000,0,1111111100000000,0,100000011000000000, %U A285781 1000000000000000,1000011110000000000,101110000000000000000,11001100000000000,10101000000000000000000,111111000000000000 %N A285781 Binary representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 94", based on the 5-celled von Neumann neighborhood. %C A285781 Initialized with a single black (ON) cell at stage zero. %D A285781 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170. %H A285781 Robert Price, Table of n, a(n) for n = 0..126 %H A285781 Robert Price, Diagrams of first 20 stages %H A285781 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015 %H A285781 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton %H A285781 S. Wolfram, A New Kind of Science %H A285781 Wolfram Research, Wolfram Atlas of Simple Programs %H A285781 Index entries for sequences related to cellular automata %H A285781 Index to 2D 5-Neighbor Cellular Automata %H A285781 Index to Elementary Cellular Automata %t A285781 CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0},{2, 1, 2}, {0, 2, 0}}, a, 2],{2}]; %t A285781 code = 94; stages = 128; %t A285781 rule = IntegerDigits[code, 2, 10]; %t A285781 g = 2 * stages + 1; (* Maximum size of grid *) %t A285781 a = PadLeft[{{1}}, {g, g}, 0,Floor[{g, g}/2]]; (* Initial ON cell on grid *) %t A285781 ca = a; %t A285781 ca = Table[ca = CAStep[rule, ca], {n, 1, stages + 1}]; %t A285781 PrependTo[ca, a]; %t A285781 (* Trim full grid to reflect growth by one cell at each stage *) %t A285781 k = (Length[ca[[1]]] + 1)/2; %t A285781 ca = Table[Table[Part[ca[[n]] [[j]],Range[k + 1 - n, k - 1 + n]], {j, k + 1 - n, k - 1 + n}], {n, 1, k}]; %t A285781 Table[FromDigits[Part[ca[[i]] [[i]], Range[i, 2 * i - 1]], 10], {i, 1, stages - 1}] %Y A285781 Cf. A285780, A285782, A285783. %K A285781 nonn,easy %O A285781 0,2 %A A285781 _Robert Price_, Apr 25 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE