The search for faster ways to get fractal pictures onto the computer screen leads to new problems on Latin squares.

Gravitational search algorithm (GSA) is one of the newest swarm based optimization algorithms, which has been inspired by the Newtonian laws of gravity and motion. GSA has empirically shown to be an efficient and robust stochastic search algorithm. Since introducing GSA a convergence analysis of this algorithm has not yet been developed. This paper introduces the first attempt to a formal conve...

Gravitational search algorithm (GSA) is one of the newest swarm based optimization algorithms, which has been inspired by the Newtonian laws of gravity and motion. GSA has empirically shown to be an efficient and robust stochastic search algorithm. Since introducing GSA a convergence analysis of this algorithm has not yet been developed. This paper introduces the first attempt to a formal conve...

We introduce an algorithm for a search of extremal fractal curves in large curve classes. It heavily uses SAT-solvers—heuristic algorithms that find models CNF boolean formulas. Our was implemented and applied to the surjective $$\gamma :[0,1]\rightarrow [0,1]^d$$ with minimal dilation $$\begin{aligned} \sup _{t_1<t_2}\frac{\Vert \gamma (t_2)-\gamma (t_1)\Vert ^d}{t_2-t_1}. \end{aligned}$$ repo...

This research investigates the efficacy of a proposed novel machine learning tool for optimal simulation building thermal load. By applying symbiotic organism search (SOS) metaheuristic algorithm to well-known model, namely an artificial neural network (ANN), sophisticated optimizable methodology is developed estimating heating load (HL) in residential buildings. Moreover, SOS comparatively ass...

In fractal image compression the encoding step is computationally expensive. A large number of sequential searches through a list of domains (portions of the image) are carried out while trying to find a best match for another image portion. Our theory developed here shows that this basic procedure of fractal image compression is equivalent to multi-dimensional nearest neighbor search. This res...

The fractal coding is a novel technique for image compression. Though the technique has many attractive features, the large encoding time makes it unsuitable for real time applications. In this paper, an efficient algorithm for fractal encoding which operates on entire domain image instead of overlapping domain blocks is presented.The algorithm drastically reduces the encoding time as compared ...