_Roger L. Bagula_, Apr 02 2005

_Roger Bagula (rlbagulatftn(AT)yahoo.com), _, Apr 02 2005

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

nonn,tabf,new

A six element substitution Triangle read by rows, based on Kenyon's tilethe morphism f: 1->2, 2->3, 3->{3,3,5,4}, 4->5, 5->6, 6->{6,6,2,1}. First row is 1. If current row is a,b,c,..., then the next row is a,b,c,...,f(a),f(b),f(c),...

1->2 2->3 3->{3,3,5,4} 4->5 5->6 6->{6,6,2,1}

s[n_] := n /. {1] = { -> 2}; s[, 2] = { -> 3}; s[, 3] = -> {3, 3, 5, 4}; s[, 4] = { -> 5}; s[, 5] = { -> 6}; s[, 6] = -> {6, 6, 2, 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, 1}, 5}]]

Cf. A073058, A103748.

nonn,uned,newtabf

See A103748 for an edited version of a similar sequence. - njas, Apr 05 2005

A six element substitution based on Kenyon's tile.

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

0,3

This substitution was suggested by looking at output of the symbols of an actual Kenyon border tiling program.

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

1->2 2->3 3->{3,3,5,4} 4->5 5->6 6->{6,6,2,1}

s[1] = {2}; s[2] = {3}; s[3] = {3, 3, 5, 4}; s[4] = {5}; s[5] = {6}; s[6] = {6, 6, 2, 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, 5}]]

Cf. A073058.

nonn,uned,new

Roger Bagula (rlbagulatftn(AT)yahoo.com), Apr 02 2005

See A103748 for an edited version of a similar sequence. - njas, Apr 05 2005

approved