Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of study area. This phenomenon has been puzzling many researchers. This paper is devoted to discussing the problem of uncertainty of fractal dimension estimation and the potential solutions to it. Using regular fractals as archety...

The project aims to explore two fractal models (by Lowen and Liebovitch) of ion channel kinetics, and how this affects spike train patterns. The project also intends to extend the Liebovitch model and explore how fractal dimension affects potassium ion channel conductance profiles, and the behavior and rate of action potentials. 1 I n t r o d u c t i o n Fractal patterns have been used to model...

A hybrid wavelet-fractal coder (WFC) for image compression is proposed. The WFC uses the fractal contractive mapping to predict the wavelet coefficients of the higher resolution from those of the lower resolution and then encode the prediction residue with a bitplane wavelet coder. The fractal prediction is adaptively applied only to regions where the rate saving offered by fractal prediction j...

Fractal property of the knowledge of supply chain is confirmed, and the concept of fractal integration is presented. And the knowledge of supply chain is fractal integrated by building modularization fractal knowledge integration network independent of the organization structure. The process of fractal integration of the knowledge is divided into five stages: acquisition, transition, applicatio...

Fractal compression schemes do not t into the standard transform coder paradigm and have proven diicult to analyze. The theory of iterated function systems motivates a broad class of fractal schemes but does not give much guidance for their implementation. We introduce a wavelet-based framework for analyzing fractal block coders which simpliies these schemes considerably. We show that fractal b...

Fractal theory has been used widely for studying the scaling properties of different biological and ecological time series [1-3]. A phenomenon showinga repeating pattern at every scale is called fractal [4]. Fractals can be regular or complex [5]. In fact, fractal objects can be characterized using a scaling exponent that is called fractal dimension. Regular and complex fractals have integer an...

Fractal functions are explored as a representation for rough data in computer graphics. Two new techniques for using fractal interpolation functions to approximate rough functions and curves are introduced. The first is based on a Hough transform of fractal function transformation parameters. The second is based on previous techniques in fractal image compression. These techniques are then demo...

Using fractal in studying tribology is becoming more important. Although digitizing and processing the surface topography image of a friction surface and wear particle are the means for calculating of the respective fractal dimensions, they are extremely troublesome. To establish a method for calculating and analyzing the fractal phenomena of a surface, the use of computer software and hardware...

SLEκ stochastic processes describe growth of random curves which, in some cases, may be identified with boundaries of two dimensional critical percolating clusters. By generalizing SLEκ growths to formal Markov processes on the central extension of the 2d conformal group, we establish a connection between conformal field theories with central charges cκ = 1 2(3κ−8)( 6 κ−1) and zero modes – obse...