Wavelet-based cascade model for intermittent structure in terrestrial environments

Abstract

A wavelet-like model for distributions of objects in natural and man-made terrestrial environments is developed. The model is constructed in a self-similar fashion, with the sizes, amplitudes, and numbers of objects occurring at a constant ratios between parent and offspring objects. The objects are randomly distributed in space according to a Poisson process. Fractal supports and a cascade model are used to organize objects intermittently in space. In its basic form, the model is for continuously varying random fields, although a level-cut is introduced to model two-phase random media. The report begins with a description of relevant concepts from fractal theory, and then progresses through static (time-invariant), steady-state, and non-steady models. The results can be applied to such diverse phenomena as turbulence, geologic distributions, urban buildings, vegetation, and arctic ice floes. The model can be used as a basis for synthesizing realistic terrestrial scenes, and for predicting the performance of sensing and communication systems in operating environments with complex, intermittent distributions of scattering objects.

Fractality in cosmic topology models with spectral action gravity

“…Example of a random fractal created by cratering (removal of discs/balls). In the example illustrated here the sequence of radii is simply taken as a n,k = 3 −n (from a geophysical model of [65]). the tangent points, in general the higher dimensional spheres have a larger intersection.…”

Fractality in Cosmic Topology Models with Spectral Action Gravity

“…Example of a random fractal created by cratering (removal of discs/balls). In the example illustrated here the sequence of radii is simply taken as a n,k = 3 −n (from a geophysical model of [63]).…”