_Roger L. Bagula_, Apr 05 2005

_Roger Bagula (rlbagulatftn(AT)yahoo.com), _, Apr 05 2005

Richard Kenyon, <a href="http://arxivarXiv.org/abs/math.MG/9505210">The Construction of Self-Similar Tilings</a>

nonn,tabf,new

11's and 12's don't do not show up until the 8th iteration, below that it resembles the lower bi-Kenyons

nonn,tabf,new

Level Triangle read by rows, based on the morphism f: 1->2, 2->3, 3->4, 4->5, 5->6, 6->{6,6 ,10,7}, 7->8, 8->9, 9->10, 10->11, 11->12, 12->{12,12,5,1}. First row is 1. If current row is a,b,c,..., then the next row is a,b,c,...,f(a),f(b-Kenyon substitution sequence),f(c),...

Level 6 bi-Kenyon substitution sequence.

1->2 2->3 3->4 4->5 5->6 6->{6,6,10,7} 7->8 8->9 9->10 10->11 12->{12,12,5,1}

s[n_] := n /. {1] = { -> 2}; s[, 2] = { -> 3}; s[, 3] = { -> 4}; s[, 4] = -> 5; s[, 5] = { -> 6} ; s[, 6] = -> {6, 6, 10, 7}; s[, 7] = { -> 8}; s[, 8] = { -> 9}; s[, 9] = { -> 10}; s[, 10] = { -> 11}; s[, 11] = { -> 12}; s[, 12] = -> {12, 12, 5, 1}}; t[a_] := Join[a, Flatten[s /@ a]]; p[0] = {1}; p[1] = t[{1}]; p[n_] := t[p[n - 1]] aa = Flatten[Table[p NestList[n], t, {n, 0, 81}, 6]]

Cf. A000120, A073058.

nonn,uned,newtabf

Level 6 b-Kenyon substitution sequence.

1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4

0,3

11's and 12's don't show up until the 8th iteration, below that it resembles the lower bi-Kenyons

Richard Kenyon, <a href="http://arxiv.org/abs/math.MG/9505210">The Construction of Self-Similar Tilings</a>

1->2 2->3 3->4 4->5 5->6 6->{6,6,10,7} 7->8 8->9 9->10 10->11 12->{12,12,5,1}

s[1] = {2}; s[2] = {3}; s[3] = {4}; s[4] = 5; s[5] = {6} ; s[6] = {6, 6, 10, 7}; s[7] = {8}; s[8] = {9}; s[9] = {10}; s[10] = {11}; s[11] = {12}; s[12] = {12, 12, 5, 1}; t[a_] := Join[a, Flatten[s /@ a]]; p[0] = {1}; p[1] = t[{1}]; p[n_] := t[p[n - 1]] aa = Flatten[Table[p[n], {n, 0, 8}]]

Cf.A000120, A073058.

nonn,uned,new

Roger Bagula (rlbagulatftn(AT)yahoo.com), Apr 05 2005

approved