Physicist Clint Sprott demonstrated a relationship between aesthetic judgments of fractal images and their fractal dimensions [1993]. Scott Draves, aka Spot, a computer scientist and artist, has created a space of images called fractal flames, based on attractors of twodimensional iterated function systems. A large community of users run software that automatically downloads animated fractal fl...

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...

Selfsimilar space-time fractal fluctuations are generic to dynamical systems in nature such as atmospheric flows, heartbeat patterns, population dynamics, etc. The physics of the long-range correlations intrinsic to fractal fluctuations is not completely understood. It is important to quantify the physics underlying the irregular fractal fluctuations for prediction of space-time evolution of dy...

Though Quantum SuperString Theory has shown promise, there are some puzzling features like the extra dimensions, which are curled up in the Kaluza-Klein sense. On the other hand a recent formulation of what may be called Quantized Fractal Space Time leads to a surprising interface with QSS we deal with the Planck length, the same number of extra dimensions and an identical non-commutative geome...

The space time that is used in relativistic Quantum Mechanics and Quantum Field Theory is the Minkowski space time. Yet, as pointed out by several scholars this classical space time is incompatible with the Heisenberg Uncertainity Principle: We cannot go down to arbitrarily small space time intervals, let alone space time points. Infact this classical space time is at best an approximation, and...

Quantifying animal movement in response to a spatially and temporally heterogeneous environment is critical to understanding the structural and functional landscape influences on population viability. Generalities of landscape structure can easily be extended to the marine environment, as marine predators inhabit a patchy, dynamic system, which influences animal choice and behavior. An innovati...

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 ...

We show that renormalization group (RG) theory applied to complex networks is useful to classify network topologies into universality classes in the space of configurations. The RG flow readily identifies a small-world-fractal transition by finding (i) a trivial stable fixed point of a complete graph, (ii) a nontrivial point of a pure fractal topology that is stable or unstable according to the...