Orbit of an Image Under Iterated System II

2013 ◽  
pp. 154-168
Author(s):  
S. L. Singh ◽  
S. N. Mishra ◽  
Sarika Jain
Keyword(s):  
Fractal Geometry ◽  
Iterative Procedure ◽  
Iterated Function System ◽  
Mathematical Structure ◽  
Computational Mathematics ◽  
Fractal Image ◽  
Iterated Function ◽  
Iterative Procedures ◽  
Modified Algorithm

An orbital picture is a mathematical structure depicting the path of an object under Iterated Function System. Orbital and V-variable orbital pictures initially developed by Barnsley (2006) have utmost importance in computer graphics, image compression, biological modeling and other areas of fractal geometry. These pictures have been generated for linear and contractive transformations using function and superior iterative procedures. In this paper, the authors introduce the role of superior iterative procedure to find the orbital picture under an IFS consisting of non-contractive or non-expansive transformations. A mild comparison of the computed figures indicates the usefulness of study in computational mathematics and fractal image processing. A modified algorithm along with program code is given to compute a 2-variable superior orbital picture.

Orbit of an Image Under Iterated System II

2011 ◽  
Vol 2 (4) ◽  
pp. 57-74
Author(s):  
S. L. Singh ◽  
S. N. Mishra ◽  
Sarika Jain
Keyword(s):  
Fractal Geometry ◽  
Iterative Procedure ◽  
Iterated Function System ◽  
Mathematical Structure ◽  
Program Code ◽  
Computational Mathematics ◽  
Fractal Image ◽  
Iterated Function ◽  
Iterative Procedures

An orbital picture is a mathematical structure depicting the path of an object under Iterated Function System. Orbital and V-variable orbital pictures initially developed by Barnsley (2006) have utmost importance in computer graphics, image compression, biological modeling and other areas of fractal geometry. These pictures have been generated for linear and contractive transformations using function and superior iterative procedures. In this paper, the authors introduce the role of superior iterative procedure to find the orbital picture under an IFS consisting of non-contractive or non-expansive transformations. A mild comparison of the computed figures indicates the usefulness of study in computational mathematics and fractal image processing. A modified algorithm along with program code is given to compute a 2-variable superior orbital picture.

A PROBABILISTIC POWER DOMAIN ALGORITHM FOR FRACTAL IMAGE DECODING

2002 ◽  
Vol 02 (02) ◽  
pp. 161-173
Author(s):  
V. DRAKOPOULOS ◽  
A. KAKOS ◽  
N. NIKOLAOU
Keyword(s):  
Complexity Analysis ◽  
Iterated Function System ◽  
Function System ◽  
Fractal Image ◽  
Power Domain ◽  
Iterated Function ◽  
Image Decoding

A new algorithm, called herein the random power domain algorithm, is discussed; it generates the image corresponding to an iterated function system with probabilities, a technique used in fractal image decoding. A simple complexity analysis for the algorithm is also derived.

scholarly journals C*-Algebras Associated with Mauldin–Williams Graphs

2008 ◽  
Vol 51 (4) ◽  
pp. 545-560 ◽  
Author(s):  
Marius Ionescu ◽  
Yasuo Watatani
Keyword(s):  
Iterated Function System ◽  
Cyclic Permutation ◽  
Invariant Set ◽  
C Algebras ◽  
Open Set ◽  
Iterated Function ◽  
Inflation Rule ◽  
Penrose Tilings ◽  
Williams Graph

AbstractA Mauldin–Williams graph is a generalization of an iterated function system by a directed graph. Its invariant set K plays the role of the self-similar set. We associate a C*-algebra (K) with a Mauldin–Williams graph and the invariant set K, laying emphasis on the singular points. We assume that the underlying graph G has no sinks and no sources. If satisfies the open set condition in K, and G is irreducible and is not a cyclic permutation, then the associated C*-algebra (K) is simple and purely infinite. We calculate the K-groups for some examples including the inflation rule of the Penrose tilings.

scholarly journals PERANCANGAN PERANGKAT LUNAK GENERATOR GAMBAR DAN MUSIK FRAKTAL DENGAN METODE ITERATED FUNCTION SYSTEM

2007 ◽  
Vol 1 (2) ◽  
pp. 140
Author(s):  
Tri Djoko Wahjono ◽  
Syaeful Karim ◽  
Bayu Riyadi
Keyword(s):  
Research Method ◽  
Iterated Function System ◽  
Function System ◽  
Clear Image ◽  
Fractal Image ◽  
Iterated Function ◽  
Art Research

Article presents analysis and analyze a software that utilize Geometry Fractal, especially Iterated FunctionSystem Fractal, as art. Research method that has been used in this research is by library study and by laboratoriumstudy to test the performance of the software. Result of the research has shown that converted music by GeometryFractal has various results, which depend on the parameters used in it and type of Geometry Fractal image produced.It can be said that usage of fractal in high iteration can produce clear image fractal and complicated music fractal.

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.

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