Theory and applications of fractal tops

Michael Barnsley

doi:10.1007/1-84628-048-6_1

Theory and applications of fractal tops

Michael Barnsley^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

15 Citations (Scopus)

Abstract

We consider an iterated function system (IFS) of one-to-one contractive maps on a compact metric space. We define the top of an IFS; define an associated symbolic dynamical system; present and explain a fast algorithm for computing the top; describe an example in one dimension with a rich history going back to work of A. Rényi [Representations for Real Numbers and Their Ergodic Properties, Acta Math. Acad. Sci. Hung., 8 (1957), pp. 477-493]; and we show how tops may be used to help to model and render synthetic pictures in applications in computer graphics.

Original language	English
Title of host publication	Fractals in Engineering
Subtitle of host publication	New Trends in Theory and Applications
Publisher	Springer London
Pages	3-20
Number of pages	18
ISBN (Print)	1846280478, 9781846280474
DOIs	https://doi.org/10.1007/1-84628-048-6_1
Publication status	Published - 2005

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10.1007/1-84628-048-6_1

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AB - We consider an iterated function system (IFS) of one-to-one contractive maps on a compact metric space. We define the top of an IFS; define an associated symbolic dynamical system; present and explain a fast algorithm for computing the top; describe an example in one dimension with a rich history going back to work of A. Rényi [Representations for Real Numbers and Their Ergodic Properties, Acta Math. Acad. Sci. Hung., 8 (1957), pp. 477-493]; and we show how tops may be used to help to model and render synthetic pictures in applications in computer graphics.

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ER -

Theory and applications of fractal tops

Abstract

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