## AIFS

 swMATH ID: 23 Software Authors: Koci\'c, Ljubi\v{s}a M. Description: A considerable class of fractal sets can be represented by using the attractors of Iterated Function Systems, with affine contractive mappings of a metric space $$(\mathbb{R}^{\nu},\text{ d})$$. The modeling capabilities of such systems are heavily limited however. For example, it is not easy to predict the location of the attractor nor its global shape. Then, Iterated Systems are not affinely invariant (affine mappings of the elements of the system do not result in affine image of its attractor). In this paper a new setting, the affine invariant Iterated Function System is described in such a way that it removes the mentioned shortcomings and can be used for shape-predictable modeling of fractal based forms. The stress is put on modeling of biological forms and their atributes such as: continuous deformation of the attractor in desired way (like in growing), branching (plants, vascular or alveolar network), gradual changing of fractal dimension from smooth to space-filling fractals. The last is useful for creating images of tissues in different stages of development, symmetry, gradual transformation from one to another form, etc. The fractal images obtained by AIFS are merely to gain resemblance to bio-forms. Homepage: http://operator.pmf.ni.ac.rs/www/pmf/publikacije/filomat/Dokumenta/15-32.pdf Keywords: iterated function systems; fractal images Related Software: Cited in: 14 Publications

### Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
AIFS-A tool for biomorphic fractal modeling. Zbl 1201.37115
Kocić, Ljubiša M.
2001
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### Cited by 25 Authors

 5 Kocić, Ljubiša M. 3 Babače, Elena 2 Castiñeira, Elena E. 2 Cubillo, Susana 1 Banchs, Albert 1 Beliakov, Gleb 1 Chang, Hsin-Hao 1 Choi, Sunghyun 1 Dutkay, Dorin Ervin 1 Ge, Ye 1 Gegovska-Zajkova, Sonja 1 Goswami, D. P. 1 Hou, Jennifer C. 1 Hwang, I-Shyan 1 Jørgensen, Palle E. T. 1 Kosek-Szott, Katarzyna 1 Mukherjee, U. K. 1 Natkaniec, Marek 1 Pach, Andrzej R. 1 Simoncelli, Alba Chiara 1 Stefanovska, Liljana 1 Torres-Blanc, Carmen 1 Vollero, Luca 1 Zabusky, Norman J. 1 Zhang, Shuang
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### Cited in 7 Serials

 3 Computer Networks 2 Information Sciences 1 Mathematische Zeitschrift 1 International Journal of Intelligent Systems 1 Filomat 1 Applied Mathematical Sciences (Ruse) 1 Nonlinear Dynamics, Psychology, and Life Sciences
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### Cited in 12 Fields

 5 Measure and integration (28-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Computer science (68-XX) 3 Mathematical logic and foundations (03-XX) 3 Numerical analysis (65-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) 1 Fluid mechanics (76-XX) 1 Biology and other natural sciences (92-XX)