Balancing order and chaos in image generation

doi:10.1016/0097-8493(93)90036-9

Computers & Graphics

Volume 17, Issue 4, July–August 1993, Pages 465-486

https://doi.org/10.1016/0097-8493(93)90036-9 Get rights and content

Abstract

We introduce new techniques to generate real-world images. Many of the natural images exhibit a hierarchical structure and a balanced combination of both order and chaos. We show how a controlled use of deterministic chaos yields a powerful method to concisely describe and to efficiently generate complex realistic images. The basic technique is the use of Mutually Recursive Function Systems (MRFS) possibly with additional control on the order of computations. Then we show that, surprisingly, regular sets of control sequences are convenient but not essential. Some examples are presented illustrating the power of the technique.

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Cited by (11)

Sur l'équivalence de descriptions de figures itérées
1996, Theoretical Computer Science
Among methods which describe and generate fractal sets we concentrate on two models, namely the recurrent sets defined by Dekking and the iterated functions system (IFS) directed by languages (here regular languages). The first model uses an endomorphism of a free semigroup, an expanding morphism from Rⁿ to Rⁿ, and maps each letter on a compact subset of Rⁿ. The second model combines contractions (from Rⁿ to Rⁿ) associated with each word (of another free semigroup) that is recognized by a finite automata and maps each accepting state to a compact subset of Rⁿ.
We give an algorithm which transforms any description in the first model into a description in the second one. So, every picture that is obtained by recurrent set method is proved to be obtained by an automata controlled IFS. We show how to build the IFS and the automata on two examples expressed in the recurrent model, namely von Koch curve and Kiesswetter curve.
Parmi les méthodes qui décrivent et engendrent des ensembles fractals, on s'intéresse à deux modèles, les ensembles récurrents définis par Dekking et les systèmes de fonctions itérées (IFS) contrôlés par des langages (ici les langages réguliers). Le premier modèle utilise un endomorphisme du monoïde libre, un morphisme expanseur de Rⁿ dans Rⁿ et associe à chaque lettre un compact de Rⁿ. Le second modèle compose des contractions associées à un mot (d'un autre monoïde libre) reconnu par un automate fini et représente chaque état terminal par un compact de Rⁿ.
On présente un algorithme transformant toute description du premier modèle en une description du second. On prouve ainsi que toute figure représentable dans le modèle des ensembles récurrents est représentable par un IFS contrôlé par automate. On montre la construction de I'IFS et de l'automate de contrôle sur deux exemples exprimés dans le modèle récurrent: la courbe de von Koch et la courbe de Kiesswetter.
Finite state transformation of images
1996, Computers and Graphics (Pergamon)
Weighted finite automata (WFA) have been introduced as devices for computing real functions on [0,1]ⁿ. The main motivation has been to generate functions on [0,1] × [0,1] interpreted as gray-tone images. Weighted finite transducers (WFT) are finite state devices that serve as a powerful tool for describing and implementing a large variety of image transformations and more generally linear operators on real functions. Here we show new results on WFT and demonstrate that WFT are indeed an excellent tool for image manipulation and more generally for function transformation. We note that every WFA transformation is a linear operator and show that most of the interesting linear operators on real functions (on [0,1]²) can be easily implemented by WFT. We give a number of examples that include affine transformations, a low-pass filter, wavelet transform, (partial) derivatives, simple and multiple integrals. Since the family of WFA-functions is constructively closed under WFT, each of our examples is actually a proof of a theorem stating that for each WFA A there effectively exists another WFA B that computes the integral (or other transformations) of the function defined by A.
Evolving fractals
1995, Computers and Graphics
Parametrized recurrent systems for image generation
1993, Information Processing Letters
We introduce Parametrized Recurrent Systems (PRS) as a tool for image generation. They are an extension of Mutually Recursive Function Systems allowing variable transformations (depending on parameters). A special case of PRS are MRFS with pasting, a very natural and convenient practical tool for image design. PRS cannot be step by step simulated by MRFS, however, we show that every PRS can be converted into an MRFS with the same number of transformations that generates the same image (attractor).
A kind of IFS fractal image generation method based on Markov random process
2019, 2019 IEEE International Conference on Computation, Communication and Engineering, ICCCE 2019
Researches on control of iterated function system attractors
2014, Lecture Notes in Electrical Engineering

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^☆: This research was supported by the National Sciences Foundation under Grant No. CCR-8702752. Preliminary version of this paper has been presented at ICALP'91, Madrid, Spain.

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Chaos and graphicsBalancing order and chaos in image generation☆

Abstract

Adv. Math.

Discrete Appl. Math.

Comp. & Graph.

J. Comp. Sys. Sci.

The Fractal Geometry of Nature

Chaos-Making a New Science

Fractals Everywhere

Harnessing chaos for image synthesis

Theory and Applications of Cellular Automata

Finite automata, quasicrystals, and Robinson tilings

Controlled disorder generated by substitutions or finite automata: The state of the art

Recurrent Sets: A Fractal Formalism

Applications of L-systems to computer imagery

Graphical applications of L-systems

Chaos and graphics
Balancing order and chaos in image generation☆