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.

References in zbMATH (referenced in 14 articles , 1 standard article )

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  1. Beliakov, G.; Bustince, H.; Goswami, D. P.; Mukherjee, U. K.; Pal, N. R.: On averaging operators for Atanassov’s intuitionistic fuzzy sets (2011)
  2. Kosek-Szott, Katarzyna; Natkaniec, Marek; Pach, Andrzej R.: A simple but accurate throughput model for IEEE 802.11 EDCA in saturation and non-saturation conditions (2011)
  3. Torres-Blanc, C.; Cubillo, S.; Castiñeira, E. E.: An axiomatic model for measuring contradiction and (\mathcalN)-contradiction between two AIFSs (2010)
  4. Babače, Elena; Kocić, Ljubiša: Minimal simplex for IFS fractal sets (2009)
  5. Castiñeira, Elena E.; Cubillo, Susana: Measures of self-contradiction on Atanassov’s intuitionistic fuzzy sets: an axiomatic model (2009)
  6. Kocić, Ljubiša; Gegovska-Zajkova, Sonja; Babače, Elena: Self-affine fractals generated by nonlinear systems (2009)
  7. Hwang, I-Shyan; Chang, Hsin-Hao: Performance assessment of IEEE 802.11e EDCF using three-dimension Markov chain model (2008)
  8. Kocić, Ljubiša; Stefanovska, Liljana; Babače, Elena: Affine invariant iterated function systems and the minimal simplex problem (2008)
  9. Dutkay, Dorin Ervin; Jorgensen, Palle E. T.: Analysis of orthogonality and of orbits in affine iterated function systems (2007)
  10. Ge, Ye; Hou, Jennifer C.; Choi, Sunghyun: An analytic study of tuning systems parameters in IEEE 802.11e enhanced distributed channel access (2007)
  11. Banchs, Albert; Vollero, Luca: Throughput analysis and optimal configuration of 802.11e EDCA (2006)
  12. Zabusky, Norman J.; Zhang, Shuang: Vortex bi-layers and the emergence of vortex projectiles in compressible accelerated inhomogeneous flows (AIFs) (2002)
  13. Kocić, Ljubiša M.: AIFS-A tool for biomorphic fractal modeling (2001)
  14. Kocić, Ljubiša M.; Simoncelli, Alba C.: Cantor dust by AIFS (2001)