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 A106147 A Levy dragon -Heighway's dragon two state 4-symbol substitution : q=1 state Levy dragon : q=0 state Heighway's dragon: Characteristic Polynomial:x^4-4*x^3+6*x^2-4*x. 0
 1, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 4, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 4, 3, 2, 2, 1, 2, 1, 1, 4, 2, 1, 1, 4, 1, 4, 4, 3, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 4, 3, 2, 2, 1, 2, 1, 1, 4, 2, 1, 1, 4, 1, 4, 4, 3, 3, 2, 2, 1, 2, 1, 1, 4, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This result shows the transform ordering is very important. This concept was inspired by the Riddle IFS that gives the Twin dragon, Levy's dragon and Heighway's dragon by rotation of one of the two transforms. LINKS F. M. Dekking, Recurrent Sets, Advances in Mathematics, vol. 44, no.1, April 1982, page 85, section 4.1. FORMULA 1->{2, 1}, 2->q*{3, 2}+(1-q}*{2, 3}, 3->{4, 3}, 4->q*{1, 4}+(1-q)*{4, 1} MATHEMATICA q=1 s[1] = {2, 1}; s[2] = q*{3, 2} + (1 - q)*{2, 3}; s[3] = {4, 3}; s[4] = q*{1, 4} + (1 - q)*{4, 1}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[8] CROSSREFS Sequence in context: A020805 A200587 A307836 * A202393 A073321 A055620 Adjacent sequences:  A106144 A106145 A106146 * A106148 A106149 A106150 KEYWORD nonn,uned AUTHOR Roger L. Bagula, May 07 2005 STATUS approved

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Last modified July 31 13:25 EDT 2021. Contains 346373 sequences. (Running on oeis4.)