In this paper the technique of particle swarm optimization (PSO) is applied for fractal image compression (FIC). With the help of this evolutionary algorithm effort is made to reduce the search complexity of matching between range block and domain block. One of the image compression techniques in the spatial domain is Fractal Image Compression but the main drawback of FIC is that it involves mo...

One important contribution has been made by Benoit Mandelbrot, the famous father of fractals who proposed a multi-fractal model of asset returns (MMAR), a theory which inherits all the hallmarks of Mandelbrot’s earlier work that has emerged since the 1970s. As a new formalization of stochastic models for the volatility dynamics of asset prices, it preserves the hierarchical multiplicative struc...

Assuming that the motions of a complex system structural units take place on continuous, but non-differentiable curves of a space-time manifold, the scale relativity model with arbitrary constant fractal dimension (the hydrodynamic and wave function versions) is built. For non-differentiability through stochastic processes of the Markov type, the non-differentiable entropy concept on a space-ti...

Digital surface representation from a set of three-dimensional samples is an important issue of computer graphics that has applications in different areas of study such as engineering, geology, geography, meteorology, medicine, etc. The digital model allows important information to be stored and analyzed without the necessity of working directly with the real surface. In addition, we can integr...

This research is the rst application of fractal compression to volumetric data. The various components of the fractal image compression method extend simply and directly to the volumetric case. However, the additional dimension increases the already high time complexity of the fractal technique, requiring the application of sophisticated volumetric block classi cation and search schemes to oper...

Many methods have been developed for structural size and configuration optimization in which cross-sectional areas are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes two efficient structural optimization methods based on the harmony search (HS) heuristic algorithm that treat both discret...

The inverse problem of fractal compression amounts to determining a contractive operator such that the corresponding fixed point approximates a given target function. The standard method based on the collage coding strategy is known to represent a suboptimal method. Why does one not search for optimal fractal codes? We will prove that optimal fractal coding, when considered as a discrete optimi...

Fractal image compression applies the self-similarity property of image. Many researches have been done to study the properties of fractal coding in image domain. In this paper, however, we try to explore the features of fractal coding in frequency domain. We rstly overview the properties of fractal coding in image domain, then we derive the corresponding formula of scaling factor and o set of ...

In this paper we apply a real analysis approach to test continuous time stochastic models of financial mathematics. Specifically, fractal dimension estimation methods are applied to statistical analysis of continuous time stochastic processes. To estimate a roughness of a sample function we modify a box-counting method typically used in estimating fractal dimension of a graph of a function. Her...

Based on an examination of K data from four different sites, a new stochastic fractal model, fractional Laplace motion, is proposed. This model is based on the assumption of spatially stationary ln(K) increments governed by the Laplace PDF, with the increments named fractional Laplace noise. Similar behavior has been reported for other increment processes (often called fluctuations) in the fiel...