DocumentCode :
3464664
Title :
IFS Matlab Generator: A Computer Tool for Displaying IFS Fractals
Author :
Tomida, Akemi Gálvez
Author_Institution :
Dept. of Appl. Math. & Comput. Sci., Univ. of Cantabria, Santander, Spain
fYear :
2009
fDate :
June 29 2009-July 2 2009
Firstpage :
132
Lastpage :
142
Abstract :
Fractals are among the most exciting and intriguing mathematical objects ever discovered. A particular type of fractals, the Iterated Function Systems (IFS), has received a lot of attention due to its appealing combination of conceptual simplicity, computational efficiency and great ability to reproduce natural formations and complex phenomena. This paper introduces a new Matlab program, called "IFS Matlab Generator", for generating and rendering IFS fractals. In addition to providing a gentle introduction to the mathematical basis of IFS, two of the most important rendering algorithms, the deterministic algorithm and the probabilistic algorithm (also called "chaos game" algorithm), are briefly outlined. A critical point of chaos game is the choice of the set of probabilities associated with the iterated functions. This issue will be briefly discussed in this paper: we analyze the efficiency of the chaos game algorithm, comparing the standard method for choosing the probabilities proposed by Michael Barnsley with another method based on a new multifractal technique. The latter method optimizes the rendering process by obtaining the most efficient set of probabilities. Some examples aimed at illustrating this technique along with a gallery of beautiful two-dimensional fractal objects are also given.
Keywords :
deterministic algorithms; fractals; mathematics computing; rendering (computer graphics); IFS Matlab Generator; IFS fractals; chaos game algorithm; deterministic algorithm; iterated function systems; mathematical objects; probabilistic algorithm; rendering algorithms; Algorithm design and analysis; Chaos; Computer displays; Economic forecasting; Fractals; Image coding; Mathematical model; Optimization methods; Rendering (computer graphics); Weather forecasting; Iterated Function Systems; attractor; dimension; fractals;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Computational Science and Its Applications, 2009. ICCSA '09. International Conference on
Conference_Location :
Yongin
Print_ISBN :
978-0-7695-3701-6
Type :
conf
DOI :
10.1109/ICCSA.2009.10
Filename :
5260935
Link To Document :
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