Computing Self-Similar Contractive Functions for the IFS Inverse Problem Through the Cuckoo Search Algorithm

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.