The fractal globule state is a popular model for describing chromatin packing in eukaryotic nuclei. Here we provide a scaling theory and dissipative particle dynamics computer simulation for the thermal motion of monomers in the fractal globule state. Simulations starting from different entanglement-free initial states show good convergence which provides evidence supporting the existence of a ...

Complexity, Risk, and Financial Markets completes a trilogy of books on chaos and fractal analysis. Fractal analysis examines self-similarity or scale invariance, a structure that is often present in seemingly random and otherwise complex processes. Time series, for example, exhibit self-similarity if subsamples resemble compressed versions of longer samples. Pioneered by engineers, mathematici...

The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored as digital image files. The computational scheme can be implemented using readily available free software. Its simplicity also makes it very interesting for...

Particle size distribution of gravelly soil plays a crucial role in debris flow initiation. For better understanding the mechanism of debris flow formation, two crucial mechanical property parameters of the gravelly soil are required to be studied meticulously: hydraulic conductivity and strength. With the aim of measuring the composition of the gravelly soil, 182 soil samples were taken from d...

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...

The fractal structure of the universe: a new field theory approach, H. Abstract While the universe becomes more and more homogeneous at large scales, statistical analysis of galaxy catalogs have revealed a fractal structure at small-scales (λ < 100h −1 Mpc), with a fractal dimension D = 1.5 − 2 (Sylos Labini et al 1996). We study the thermodynamics of a self-gravitating system with the theory o...

The author proposes an independent and novel approach to image coding, based on a fractal theory of iterated transformations. The main characteristics of this approach are that (i) it relies on the assumption that image redundancy can be efficiently exploited through self-transformability on a block-wise basis, and (ii) it approximates an original image by a fractal image. The author refers to ...

Fractal image compression successfully uses selfsimilarity within an image to achieve compression. By adapting fractal image compression techniques to image enhancement, an innovative new fractal technique for visual enhancement of JPEG compressed images is created. After detecting the self-similarity characteristics of a degraded JPEG image, details spoiled by quantization are enhanced using a...

Abstract The image inpainting is an important problem image processing. It is a difficult problem to recover an image with bigger hole, and the existing algorithms are not give good method. Based on fractal theory, in this paper, we present a new inpainting method, which using the total info of image effectively. The relation of fractal dimension and the size range block is discussed, and give ...

Characterization of a digitized image is often required in nondestructive evaluation. Apart from the existing image processing techniques, a recent method to analyze and quantify complex images has been developed based on the fractal theory. As reported, it is possible to get salient information from any digitized image by evaluating the fractal dimension, the defining characteristic of a fract...