Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of advantage. Geometry is ideally suited for expressing the logic of evolutionary selection for symmetry, which is found in the shape curves of vein systems an...

A notion which has been advanced intensively in the past two decades, is that fractal geometry describes well the irregular face of Nature. We were prompted by Marder’s recent article in Science [1], to comment here on the applicability of this wide-spread notion. Marder summarizes a simulation study of fractured silicon nitride by Kalia et. al [2] which successfully mimics experimental data, a...

During this decade, the design of small-size wireless communication devices was key topic in the field of communication engineering. The design of miniaturized antenna is an important parameter to reduce the overall size of the wireless communication devices. Many approaches have been proposed to design the miniaturized antennas. Recently, fractal antenna geometry has been employed to design th...

Self-similarity is a concept often associated with fractal geometry. There are many interesting self-similar sets in the plane which would not generally be considered fractal, however (although their boundaries might be fractal). Such sets provide a fresh way of looking at tilings of the plane. Furthermore, a generalization of self-similarity, called digraph self-similarity, provides a way to c...

Analysis of highly iterated fractal antennas using integral equation methods is addressed in this paper. Time and memory requirements are greatly reduced taking advantage of the recursive structure of the fractal geometry.

As a new modeling procedure of geothermal energy extraction systems, the authors present two dimensional and three dimensional modeling techniques of subsurface fracture network, based on fractal geometry. Fluid flow in fractured rock occurs primarily through a connected network of discrete fractures. The fracture network approach, therefore, seeks to model fluid flow and heat transfer through ...

Moran’s Theorem is one of the milestones in Fractal Geometry. It allows the calculation of the similarity dimension of any (strict) self-similar set lying under the open set condition. Throughout a new fractal dimension we provide in the context of fractal structures, we generalize such a classical result for attractors which are required to satisfy no separation properties.

A fractal set which corresponds to the six-vertex model has been obtained and a relationship between the free energy of the six-vertex model and the fractal dimension of the fractal set was established. Notions which correspond to the transfer matrix and the n-equivalence has been found in the area of the fractal geometry. This correspondence can be generalized to the case of the models suitabl...

Recent studies have shown that fractal geometry, a vocabulary of irregular shapes, can be useful for describing the pathological architecture of tumors and, perhaps more surprisingly, for yielding insights into the mechanisms of tumor growth and angiogenesis that complement those obtained by modern molecular methods. This article outlines the basic methods of fractal geometry and discusses the ...

The advent of the computer age played an important role in the development and acceptance of fractal geometry as a valid new discipline. New insights gained from the application of fractal geometry to ecology include: understanding the importance of spatial and temporal scales; the relationship between landscape structure and movement pathways; an increased understanding of landscape structures...