HIGHER BLOCK IFS 1: MEMORY REDUCTION AND DIMENSION COMPUTATIONS-Reference-Cited by-同舟云学术

HIGHER BLOCK IFS 1: MEMORY REDUCTION AND DIMENSION COMPUTATIONS

Published:2010-06 Issue:02 Volume:18 Page:145-155
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

BEDIENT RICHARD¹,FRAME MICHAEL²,GROSS KEITH¹,LANSKI JENNIFER,SULLIVAN BRENDAN³

Affiliation:

1. Mathematics Department, Hamilton College, Clinton, NY 13323, USA

2. Mathematics Department, Yale University, 10 Hillhouse Ave., P. O. Box 208283, New Haven, CT 06520-8283, USA

3. Mathematics Department, Carnegie Mellon University, Pittsburgh, PA 15213, USA

Abstract

By applying a result from the theory of subshifts of finite type,1 we generalize the result of Frame and Lanski2 to IFS with multistep memory. Specifically, we show that for an IFS [Formula: see text] with m-step memory, there is an IFS with 1-step memory (though in general with many more transformations than [Formula: see text]) having the same attractor as [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X10004804

Reference22 articles.

1. An Introduction to Symbolic Dynamics and Coding

2. WHEN IS A RECURRENT IFS ATTRACTOR A STANDARD IFS ATTRACTOR?

3. Chaos automata: iterated function systems with memory

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1. Fractal and multifractal geometry: scaling symmetry and statistics;Wiley Interdisciplinary Reviews: Computational Statistics;2012-03-22

2. HIGHER BLOCK IFS 2: RELATIONS BETWEEN IFS WITH DIFFERENT LEVELS OF MEMORY;Fractals;2010-12

3. MULTIFRACTAL MEASURES OF TIME SERIES: f(α) SURFACES;International Journal of Bifurcation and Chaos;2010-08