Symbolic Dynamics for IFS Attractors

It has recently been shown that a modified iterated function system (IFS) is capable of generating closed orbits which undergo bifurcation and transition to a chaotic regime as control parameters are varied.1,2 Here we show that driving such an IFS by a partition of itself creates maps which can be characterized by a symbolic dynamics. Forbidden words are determined for this dynamics under various parameter values, and the implications of this mapping are discussed.

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Orbits Embedded in IFS Attractors

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127497000534 ◽

1997 ◽

Vol 07 (03) ◽

pp. 741-749 ◽

Cited By ~ 2

Author(s):

Sonya Bahar

Keyword(s):

Iterated Function System ◽

Chaotic Regime ◽

Function System ◽

Chaotic Attractors ◽

Control Parameters ◽

Closed Orbits ◽

Iterated Function

It has recently been shown that a modified iterated function system (IFS) is capable of generating closed orbits which undergo bifurcation and transition to a chaotic regime as control parameters are varied [Bahar, 1995, 1996]. Here we discuss a technique for isolating orbits embedded in chaotic attractors generated by an IFS algorithm, and develop a symbolic classification based on the folding patterns of the embedded orbits.

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An improved fractal image compression approach by using iterated function system and genetic algorithm

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2006.05.010 ◽

2006 ◽

Vol 51 (11) ◽

pp. 1727-1740 ◽

Cited By ~ 10

Author(s):

Yang Zheng ◽

Guanrong Liu ◽

Xiaoxiao Niu

Keyword(s):

Genetic Algorithm ◽

Image Compression ◽

Iterated Function System ◽

Function System ◽

Fractal Image Compression ◽

Fractal Image ◽

Iterated Function

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ARCLENGTH AS THE INVARIANT MEASURE FOR AN IFS WITH PROBABILITIES

Fractals ◽

10.1142/s0218348x15500462 ◽

2015 ◽

Vol 23 (04) ◽

pp. 1550046

Author(s):

D. LA TORRE ◽

F. MENDIVIL

Keyword(s):

Invariant Measure ◽

Iterated Function System ◽

Function System ◽

Iterated Function

Given a continuous rectifiable function [Formula: see text], we present a simple Iterated Function System (IFS) with probabilities whose invariant measure is the normalized arclength measure on the graph of [Formula: see text].

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Stochastic Fractal Modeling and Process Planning for Machining Using Two-Dimensional Iterated Function System

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.392-394.575 ◽

2008 ◽

Vol 392-394 ◽

pp. 575-579

Author(s):

Yu Hao Li ◽

Jing Chun Feng ◽

Y. Li ◽

Yu Han Wang

Keyword(s):

Path Planning ◽

Tool Path ◽

Iterated Function System ◽

Numerical Control ◽

Function System ◽

Tool Path Planning ◽

Ongoing Research ◽

Iterated Function ◽

Planning Algorithm ◽

Path Planning Algorithm

Self-affine and stochastic affine transforms of R2 Iterated Function System (IFS) are investigated in this paper for manufacturing non-continuous objects in nature that exhibit fractal nature. A method for modeling and fabricating fractal bio-shapes using machining is presented. Tool path planning algorithm for numerical control machining is presented for the geometries generated by our fractal generation function. The tool path planning algorithm is implemented on a CNC machine, through executing limited number of iteration. This paper describes part of our ongoing research that attempts to break through the limitation of current CAD/CAM and CNC systems that are oriented to Euclidean geometry objects.

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Using artificial neural network for the calculation of iterated function system codes

Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94) ◽

10.1109/icnn.1994.374860 ◽

1994 ◽

Author(s):

A.W.H. Lee ◽

L.M. Cheng

Keyword(s):

Neural Network ◽

Artificial Neural Network ◽

Iterated Function System ◽

Function System ◽

Iterated Function ◽

Artificial Neural

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Modelling of tree crowns with realistic morphological features: New reconstruction methodology based on Iterated Function System tool

Ecological Modelling ◽

10.1016/j.ecolmodel.2010.10.002 ◽

2011 ◽

Vol 222 (3) ◽

pp. 503-513 ◽

Cited By ~ 9

Author(s):

A. Collin ◽

A. Lamorlette ◽

D. Bernardin ◽

O. Séro-Guillaume

Keyword(s):

Iterated Function System ◽

Morphological Features ◽

Function System ◽

Tree Crowns ◽

Iterated Function

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A graphical representation of protein based on a novel iterated function system

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2014.01.067 ◽

2014 ◽

Vol 403 ◽

pp. 21-28 ◽

Cited By ~ 22

Author(s):

Tingting Ma ◽

Yuxin Liu ◽

Qi Dai ◽

Yuhua Yao ◽

Ping-an He

Keyword(s):

Graphical Representation ◽

Iterated Function System ◽

Function System ◽

Iterated Function

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Fractal dimension and iterated function system (IFS) for speech recognition

Electronics Letters ◽

10.1049/el:19920879 ◽

1992 ◽

Vol 28 (15) ◽

pp. 1382 ◽

Cited By ~ 6

Author(s):

E.L.J. Bohez ◽

T.R. Senevirathne ◽

J.A. van Winden

Keyword(s):

Fractal Dimension ◽

Speech Recognition ◽

Iterated Function System ◽

Function System ◽

Iterated Function

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Fractal set of Generalized Countable Partial Iterated Function System with Generalized Contractions via Partial Hausdorff Metric

Topology and its Applications ◽

10.1016/j.topol.2022.108000 ◽

2022 ◽

pp. 108000

Author(s):

M. Priya ◽

R. Uthayakumar

Keyword(s):

Iterated Function System ◽

Hausdorff Metric ◽

Function System ◽

Fractal Set ◽

Iterated Function ◽

Partial Hausdorff Metric

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Fractal Top for Contractive and Non-Contractive Transformations

International Journal of Artificial Life Research ◽

10.4018/ijalr.2012100104 ◽

2012 ◽

Vol 3 (4) ◽

pp. 49-65

Author(s):

Sarika Jain ◽

S. L. Singh ◽

S. N. Mishra

Keyword(s):

Fixed Point ◽

Iterated Function System ◽

Function System ◽

Feedback Process ◽

Iterated Function ◽

Spatial Part ◽

One Step ◽

The One ◽

Definition Of

Barnsley (2006) introduced the notion of a fractal top, which is an addressing function for the set attractor of an Iterated Function System (IFS). A fractal top is analogous to a set attractor as it is the fixed point of a contractive transformation. However, the definition of IFS is extended so that it works on the colour component as well as the spatial part of a picture. They can be used to colour-render pictures produced by fractal top and stealing colours from a natural picture. Barnsley has used the one-step feed- back process to compute the fractal top. In this paper, the authors introduce a two-step feedback process to compute fractal top for contractive and non-contractive transformations.

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