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1996/1997 Self-affine curves and sequential machines
Heinz-Otto Peitgen, Anna Rodenhausen, Gencho Skordev
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Real Anal. Exchange 22(2): 446-491 (1996/1997).


Our paper was motivated by the desire to understand to what extend the notion of sequential functions is capable to construct self-affine functions and curves. We shall prove that each self-affine curve is generated by a sequential machine. This includes not only the curves obtained by the method of M. F. Dekking but also curves produced by iterated function systems. In order to expose the relations between the construction using sequential functions and the previous established methods we introduce several types of self-affine curves. Many classical examples will be discussed to illustrate the different types of self-affinity. In the general case, the realization of the curves by means of sequential functions is based on the classical Cantor representation of the real numbers in the unit interval. The combinatorial part of Dekking’s construction, the substitution, will appear as an ingredient of the sequential machine. The geometrical part can be recovered in the consistency condition for sequential machines, which assures that a sequential machine leads to a continuous function.


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Heinz-Otto Peitgen. Anna Rodenhausen. Gencho Skordev. "Self-affine curves and sequential machines." Real Anal. Exchange 22 (2) 446 - 491, 1996/1997.


Published: 1996/1997
First available in Project Euclid: 22 May 2012

zbMATH: 0937.68072
MathSciNet: MR1460970

Primary: 26A27 , 68Q68
Secondary: 26A30 , 54H20‎ , 68Q42

Keywords: finite automata , iterated function systems , L-systems , self-affine curves , self-affine functions , sequential functions , sequential machines

Rights: Copyright © 1996 Michigan State University Press

Vol.22 • No. 2 • 1996/1997
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