scholarly journals Visualization of the Chaos Game for non-hyperbolic iterated function system

2020 ◽  
Vol 1 (2) ◽  
pp. 9-20
Author(s):  
Pablo José Mavares Ferrer
Keyword(s):  
Dynamic System ◽  
Iterated Function System ◽  
Point Of View ◽  
Function System ◽  
Application Point ◽  
Iterated Function ◽  
Random Algorithm ◽  
Chaos Game ◽  
Mathematical Didactics

The chaos game is a random algorithm generally applied to contracting (hyperbolic) iterated function system (IFS) which makes it possible to obtain the unique attractor of the dynamic system. However, when applied to non-contractive IFS extremely interesting results can be obtained that are not only important from a theoretical and application point of view, but can also be part of a mathematical didactics that seeks to modernize teaching. In this sense, this research present some results related to the application of the chaos game to non-contracting IFS are presented.

scholarly journals The Chaos Game on a General Iterated Function System from a Topological Point of View

2014 ◽  
Vol 24 (11) ◽  
pp. 1450139 ◽  
Author(s):  
Michael F. Barnsley ◽  
Krzysztof Leśniak
Keyword(s):  
Stochastic Process ◽  
Iterated Function System ◽  
Almost Sure Convergence ◽  
Baire Category ◽  
Point Of View ◽  
Function System ◽  
Iterated Function ◽  
Chaos Game

We investigate combinatorial issues relating to the use of random orbit approximations to the attractor of an iterated function system with the aim of clarifying the role of the stochastic process during the generation of the orbit. A Baire category counterpart of almost sure convergence is presented.

A NEW EXAMPLE OF A DETERMINISTIC CHAOS GAME

2016 ◽  
Vol 94 (3) ◽  
pp. 464-470 ◽  
Author(s):  
ALIASGHAR SARIZADEH
Keyword(s):  
Iterated Function System ◽  
Deterministic Chaos ◽  
Function System ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Iterated Function ◽  
Chaos Game ◽  
Necessary And Sufficient

We give a new necessary and sufficient condition for an iterated function system to satisfy the deterministic chaos game. As a consequence, we give a new example of an iterated function system which satisfies the deterministic chaos game.

scholarly journals The chaos game on a general iterated function system

2010 ◽  
Vol 31 (4) ◽  
pp. 1073-1079 ◽  
Author(s):  
MICHAEL F. BARNSLEY ◽  
ANDREW VINCE
Keyword(s):  
Iterated Function System ◽  
General Setting ◽  
Iterated Function Systems ◽  
Function System ◽  
Iterated Function ◽  
Chaos Game ◽  
Weaker Conditions

AbstractThe main theorem of this paper establishes conditions under which the ‘chaos game’ algorithm almost surely yields the attractor of an iterated function system. The theorem holds in a very general setting, even for non-contractive iterated function systems, and under weaker conditions on the random orbit of the chaos game than obtained previously.

ARCLENGTH AS THE INVARIANT MEASURE FOR AN IFS WITH PROBABILITIES

Fractals ◽  
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].

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

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.

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

1992 ◽  
Vol 28 (15) ◽  
pp. 1382 ◽  
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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