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A106147
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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.
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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; internal format)
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OFFSET
| 0,2
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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.
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REFERENCES
| F. M. Dekking, "Recurrent Sets", Advances in Mathematics, vol. 44, no.1, April 1982, page 85, section 4.1
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FORMULA
| 1->{2, 1}, 2->q*{3, 2}+(1-q}*{2, 3}, 3->{4, 3}, 4->q*{1, 4}+(1-q)*{4, 1}
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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]
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CROSSREFS
| Sequence in context: A073261 A020805 A200587 * A202393 A073321 A055620
Adjacent sequences: A106144 A106145 A106146 * A106148 A106149 A106150
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KEYWORD
| nonn,uned
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), May 07 2005
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