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

Access to Document

10.1007/1-84628-048-6_1

Cite this

@inbook{5d42103e14dd42bc9117a9aecdc8fd5c,

title = "Theory and applications of fractal tops",

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. R{\'e}nyi [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.",

author = "Michael Barnsley",

year = "2005",

doi = "10.1007/1-84628-048-6_1",

language = "English",

isbn = "1846280478",

pages = "3--20",

booktitle = "Fractals in Engineering",

publisher = "Springer London",

address = "United Kingdom",

}

TY - CHAP

T1 - Theory and applications of fractal tops

AU - Barnsley, Michael

PY - 2005

Y1 - 2005

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=34247593557&partnerID=8YFLogxK

U2 - 10.1007/1-84628-048-6_1

DO - 10.1007/1-84628-048-6_1

M3 - Chapter

SN - 1846280478

SN - 9781846280474

SP - 3

EP - 20

BT - Fractals in Engineering

PB - Springer London

ER -

Theory and applications of fractal tops

Abstract

Access to Document

Other files and links

Fingerprint

Cite this