Abstract
One of the most powerful and popular methods to generate fractal images is the so-called iterated function systems (IFS). Given a finite system of contractive maps \(\{w_i\}_{i=1,\dots ,n}\) on the compact metric space \(\mathbb {R}^2\), this system has a unique non-empty compact fixed set \(\mathcal {A}\), called the attractor of the IFS. The graphical representation of this attractor is a self-similar fractal image. The opposite is also true: each self-similar fractal image in \(\mathbb {R}^2\) can be mathematically represented as the only attractor of an IFS. Obtaining the parameters of the IFS system (called the IFS inverse problem) is a very difficult issue. A good strategy to address it consists of solving firstly the sub-problem of computing a suitable set of self-similar contractive functions to be further applied to obtain the optimal IFS for the inverse problem. In this paper we address this sub-problem by using a powerful metaheuristic technique called cuckoo search algorithm. Our experimental results show that the method performs quite well for several self-similar fractal images.
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Acknowledgements
This research has been kindly supported by the Computer Science National Program of the Spanish Ministry of Economy and Competitiveness, Project Ref. #TIN2012-30768, Toho University, and the University of Cantabria.
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Quirce, J., Gálvez, A., Iglesias, A. (2017). Computing Self-Similar Contractive Functions for the IFS Inverse Problem Through the Cuckoo Search Algorithm. In: Del Ser, J. (eds) Harmony Search Algorithm. ICHSA 2017. Advances in Intelligent Systems and Computing, vol 514. Springer, Singapore. https://doi.org/10.1007/978-981-10-3728-3_33
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DOI: https://doi.org/10.1007/978-981-10-3728-3_33
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