Fractal dimension has been found not suitable to be used solely in classifying natural earth terrain. This is due to the fact that surfaces with different texture may portray similar fractal dimensions. Evertsz and Mandelbrot [Evertsz, et. al. 1992] suggested that multifractal dimension may be a more appropriate parameter than fractal dimension in describing geometrical properties of a fractal ...

A random sequential box-covering algorithm recently introduced to measure the fractal dimension in scale-free (SF) networks is investigated. The algorithm contains Monte Carlo sequential steps of choosing the position of the center of each box; thereby, vertices in preassigned boxes can divide subsequent boxes into more than one piece, but divided boxes are counted once. We find that such box-s...

In recent work, various fractal image coding methods are reported, which adopt the selfsimilarity of images to compress the size of images. However, till now, no solutions for the security of fractal encoded images have been provided. In this paper, a secure fractal image coding scheme is proposed and evaluated, which encrypts some of the fractal parameters during fractal encoding, and thus, pr...

The Invariant Set Hypothesis proposes that states of physical reality belong to, and are governed by, a non-computable fractal subset I of state space, invariant under the action of some subordinate deterministic causal dynamics I D . The Invariant Set Hypothesis is motivated by key results in nonlinear dynamicalsystems theory, and black-hole thermodynamics. The elements of a reformulation of q...

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...

In this paper we propose the optimization of patch size for a fractal hybrid antenna that can be used in GPS applications. This project is about two different models namely sierpinski gasket fractal antenna and Koch rectangular fractal antenna. A fractal antenna in general is characterized by space filling and self-similarity properties. These fractal shaped antennas have their own unique chara...

In this paper, the optical properties of one dimensional fractal structures are investigated. We consider six typical fractal photonic structures: the symmetric dual cantor-like fractal structure, the asymmetric dual cantor-like fractal structure, the single cantor-like fractal structure, the symmetric dual golden-section fractal structure, the asymmetric dual golden-section fractal structure a...