Inversion Fractals and Iteration Processes in the Generation of Aesthetic Patterns

In this paper, we generalize the idea of star‐shaped set inversion fractals using iterations known from fixed point theory. We also extend the iterations from real parameters to so‐called q‐system numbers and proposed the use of switching processes. All the proposed generalizations allowed us to obt...

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Bibliographic Details
Published in:Computer graphics forum Vol. 36; no. 1; pp. 35 - 45
Main Author: Gdawiec, K.
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.01.2017
Subjects:
aesthetic pattern
Algorithms
Ceramics
Chaos theory
fractal
Fractal analysis
Fractals
G.1.2 [Mathematics and Computing]: Approximation—Wavelets and fractals; I.3.5 [Computer Graphics]: Computational geometry and object modelling—Geometric algorithms
Games
generative art
inversion
Inversions
iteration
Iterative methods
languages and systems; I.3.m [Computer Graphics]: Miscellaneous
Mathematical analysis
Switching
Textiles
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:In this paper, we generalize the idea of star‐shaped set inversion fractals using iterations known from fixed point theory. We also extend the iterations from real parameters to so‐called q‐system numbers and proposed the use of switching processes. All the proposed generalizations allowed us to obtain new and diverse fractal patterns that can be used, e.g. as textile and ceramics patterns. Moreover, we show that in the chaos game for iterated function systems—which is similar to the inversion fractals generation algorithm—the proposed generalizations do not give interesting results. In this paper, we generalize the idea of star‐shaped set inversion fractals using iterations known from fixed point theory. We also extend the iterations from real parameters to so‐called q‐system numbers and proposed the use of switching processes. All the proposed generalizations allowed us to obtain new and diverse fractal patterns that can be used, e.g. as textile and ceramics patterns. Moreover, we show that in the chaos game for iterated function systems—which is similar to the inversion fractals generation algorithm—the proposed generalizations do not give interesting results.
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12783