A106638 3-symbol substitution that gives a dragon fractal.

1, 2, 2, 1, 2, 3, 3, 2, 2, 3, 3, 2, 1, 2, 2, 1, 2, 3, 3, 2, 3, 1, 1, 3, 3, 1, 1, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 1, 1, 3, 3, 1, 1, 3, 2, 3, 3, 2, 1, 2, 2, 1, 2, 3, 3, 2, 2, 3, 3, 2, 1, 2, 2, 1, 2, 3, 3, 2, 3, 1, 1, 3, 3, 1, 1, 3, 2, 3, 3, 2, 3, 1, 1, 3, 1, 2, 2, 1, 1, 2, 2, 1, 3, 1, 1, 3, 3, 1, 1, 3, 1, 2, 2, 1, 1

Offset

0,2

Links

Table of n, a(n) for n=0..104.

Formula

1->{1, 2, 2, 1}, 2->{2, 3, 3, 2}, 3->{3, 1, 1, 3}

Mathematica

s[1] = {1, 2, 2, 1}; s[2] = {2, 3, 3, 2}; s[3] = {3, 1, 1, 3}; t[a_] := Flatten[s /@ a] p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[4]
SubstitutionSystem[{1->{1, 2, 2, 1}, 2->{2, 3, 3, 2}, 3->{3, 1, 1, 3}}, {1}, {5}][[1]] (* Harvey P. Dale, Feb 06 2022 *)

Crossrefs

Sequence in context: A337225 A256478 A356245 * A329400 A131909 A307319

Adjacent sequences: A106635 A106636 A106637 * A106639 A106640 A106641

Keyword

nonn,uned

Author

Roger L. Bagula, May 11 2005

Extensions

Corrected formula - Jon Perry, Oct 08 2012

Status

approved