Abstract
It is proved that the maximum value of the ratio |p(x) − p(y)|2/|x − y| for the Peano-Hilbert curve p: [0, 1] = I → I 2 is equal to 6.
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E. V. Shchepin and K. E. Bauman, “On Peano curves of fractal genus 9,” in: Modeling and Analysis of Data [in Russian], Proceedings of the Faculty of Informational Technologies, Moscow City Psychological-Pedagogical University, issue 1, Rusavia, Moscow, 2004, pp. 78–89.
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Translated from Matematicheskie Zametki, vol. 80, no. 5, 2006, pp. 643–656.
Original Russian Text Copyright © 2006 by K. E. Bauman.
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Bauman, K.E. The dilation factor of the Peano-Hilbert curve. Math Notes 80, 609–620 (2006). https://doi.org/10.1007/s11006-006-0182-8
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DOI: https://doi.org/10.1007/s11006-006-0182-8