Compression and decompression tools of digital image has become a significant aspect in the storing and transferring of digital image. Fractal image compression technique is recently used to compress images. The main problem with fractal image compression is that it takes a lot of computational time for searching blocks (domain block and range block) and then compares these blocks. There are ma...

Fractal behavior and long-range dependence have been observed in an astonishing number of physical, biological, geological, and socio-economic systems. Time series, profiles, and surfaces have been characterized by their fractal dimension, a measure of roughness, and by the Hurst coefficient, a measure of long-memory dependence. Either phenomenon has been modeled and explained by self-affine ra...

Robot navigasyonunun en önemli bileşenlerinden biri olan yol planlama son yıllarda da araştırmacılar tarafından kapsamlı bir şekilde incelenmekte ve bu problem için birçok farklı metasezgisel algoritma kullanılmaktadır. Bu çalışmada ızgara tipi ortamda mobil robotun küresel planlaması ele alınmış matematik tabanlı algoritmalarının etkileri incelenmiştir. Öncelikle tipinde zorluk derecelerinde ü...

The Kardar-Parisi-Zhang (KPZ) equation has been connected to a large number of important stochastic processes in physics, chemistry and growth phenomena, ranging from classical quantum physics. central quest this field is the search for ever more precise universal exponents. Notably, exact exponents are only known $1+1$ dimensions. In work, we present physical geometric analytical methods that ...

In this paper we construct three primitive mappings based on three kinds of genetic attribute equivalences. We then apply the mappings and basic addition operation to the universal genetic code to generate three square matrices. We show that these square matrices are stochastic in nature. They demonstrate some fractal similarity properties and resemble the similar properties to the original sto...

Fractal image compression is based on the rather poorly motivated assumption that “natural” images exhibit significant affine self-similarity. The accuracy of this assumption is evaluated by a comparison between the statistics of natural images and those of a multiresolution stochastic model designed to generate images exhibiting affine self-similarity as assumed by fractal coding techniques. T...

The paper suggests a generalisation of the diffusion-limited aggregation (DLA) based on using a general stochastic process to control particle movements before sticking to a growing cluster. This leads to models with variable characteristics that can provide a single framework for treating a number of earlier models of fractal growth: the DLA, the Eden model and the ballistic aggregation. Addit...

In this study, a novel fractal watermarking is proposed to enforce the robustness of data hiding against possible attack. The proposed fractal watermarking is mixed of three different approaches: inner/exterior search space, odd/even search space, and two classes of isometric search space. During watermark extraction, the watermark bit is always determined by the result of a voting mechanism on...