Open Access
2000/2001 Computational Complexity of Fractal Sets
Kamo Hiroyasu, Takeuti Izumi, Kawamura Kiko
Real Anal. Exchange 26(2): 773-794 (2000/2001).


In studies on fractal geometry, it is important to determine whether the classification by means of computational complexity is independent of the classification by means of fractal dimension. In this paper, we show that each self-similar set defined by polynomial time computable functions is polynomial time computable, if the self-similar set satisfies a polynomial time open set condition. This fact provides us examples of sets whose computational complexity are polynomial time computable, and which have non integer Hausdorff dimension. We also construct a set with computational complexity NP-complete and with an integer Hausdorff dimension. These two examples establish the independence of computational complexity and Hausdorff dimension.


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Kamo Hiroyasu. Takeuti Izumi. Kawamura Kiko. "Computational Complexity of Fractal Sets." Real Anal. Exchange 26 (2) 773 - 794, 2000/2001.


Published: 2000/2001
First available in Project Euclid: 27 June 2008

zbMATH: 1009.68059
MathSciNet: MR1844393

Primary: 03D15 , 03F60 , 28A80 , 68Q25

Keywords: Fractals , self-similar sets , Time complexity

Rights: Copyright © 2000 Michigan State University Press

Vol.26 • No. 2 • 2000/2001
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