Nowadays more and more aesthetic product developments, assemblage and decoration designs are taking aesthetically appealing forms of natural objects such as rough terrain, ripples on lakes, coastline and seafloor topography. They are mathematical definable via fractal geometry theory and emerge to attract a lot of attention. However, not many methods for manufacturing of fractal objects have be...

We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1 < h < 2, a fractal distribution function associated with a fractal von Newmann entropy. Fractons are charge-flux systems defined in two-dimensional multiply connected space and they carry rational or irrational ...

A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and spatial network proved to be associated with one another. This paper is devoted to exploring the theory of fractal analysis of complex systems by means of hierar...

We investigate in this work a local version of the theory of fractal strings and associated geometric zeta functions. Such a generalization allows to describe the asymptotic behaviour of a “fractal” set in the neighborhood of any of its points. We give basic properties and several examples illustrating the possible range of situations concerning in particular the evolution of the local complex ...

Jessica L. Green*, John Harte and Annette Ostling Department of Environmental Science and Policy, University of California, One Shields Avenue, Davis, CA 95616, USA Energy and Resources Group, University of California, Berkeley, CA 94720, USA *Correspondence: E-mail: [email protected] Abstract Although scaling relationships that characterize fractal species distributions offer an exciting pot...

in this work, sio2 –zro2 mixed oxides was prepared by the polymeric sol–gel route. the characterization of pore structure, which determines the permeation process of membrane, is of great importance. so far, most investigations have focused on such pore structure as specific surface area and pore size distribution, but the surface fractal, the important parameter reflecting the roughness of por...

Fractal image compression was one of the earliest compression schemes to take advantage of image redundancy in scale. The theory of iterated function systems motivates a broad class of fractal schemes but does not give much guidance for implementation. Fractal compression schemes do not t into the standard transform coder paradigm and have proven di cult to analyze. We introduce a wavelet-based...

To process the vibration signal fault diagnosis automatically and effectively, a method to calculate the generalized fractal dimension (Dq) based on the traditional G-P correlation dimension algorithm is presented. First, the vibration signal, a kind of random fractal that meets the statistical self-similarity, is reconstructed according to the phase space reconstruction theory. Second, for var...

In this book, the author proposes a new approach to understand and possibly solve the Riemann Hypothesis. His reformulation builds upon earlier (joint) work on complex fractal dimensions and the vibrations of fractal strings, combined with string theory and noncommutative geometry. Accordingly, it relies on the new notion of a fractal membrane or quantized fractal string, along with the modular...

We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1 < h < 2, a fractal distribution function associated with a fractal von Newmann entropy. Fractons are charge-flux systems defined in two-dimensional multiply connected space and they carry rational or irrational ...