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On Takagi Fractal Surfaces

Part of: Functions of several variables

Published online by Cambridge University Press:  20 November 2018

Benoit Dubuc
Benoit Dubuc*
Affiliation:
Dept. of Electrical Engineering Computer Vision and Robotics Lab. McGill University Montreal, PQ, H3A 2A7
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Abstract

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This paper presents a new type of fractal surfaces called the Takagi surfaces. These are obtained by summing up pyramids of increasing (doubling) frequencies scaled by a geometric ratio b. The fractal dimension (box dimension) of the graph of these functions is shown to be log 8b/log 2.

MSC classification

Secondary: 26B35: Special properties of functions of several variables, Hölder conditions, etc.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 3 , 01 September 1989 , pp. 377 - 384
Copyright
Copyright © Canadian Mathematical Society 1989

References

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