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On the differentiability of the coordinate functions of Póyla's space-filling curve

✍ Scribed by Karl Prachar; Hans Sagan

Publisher
Springer Vienna
Year
1996
Tongue
English
Weight
493 KB
Volume
121
Category
Article
ISSN
0026-9255

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Based on a parametrization of Hilbert's space-$lling curve that was recently found by this author, an analytic proof of the nowhere dijjerentiability of the coordinate functions of that curve is presented. '$.> The Franklinlnstitute0016-0032/93 %6.00+000

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In his paper [l] P6lya defines the following function P, mapping the interval [0, I] onto a right triangle T. Let t be any number in the unit interval; expand it into a binary fraction: t = .d,d, ... The n-th digit d,(t) of t is either 0 or 1. For each t we assign a sequence of nested triangles T