We investigate the interplay between geometry and iterated function systems in families of three-dimensional fractal trees. ! 2008 Elsevier Ltd. All rights reserved.

This essay concerns fractal geometry as a bridge between the imaginary and the real, mind and matter, conscious and unconscious. The logic rests upon Jung’s theory of number as the most primitive archetype of order for linking observers with the observed. Whereas Jung focused upon natural numbers as the foundation for order that is already conscious, I offer fractal geometry, with its endlessly...

The high complexity of remotely sensed images and measurements, provided by the last generation of sensors, demands new techniques for scene understanding and analysis. The paper introduces topics in multisensor and synthetic images fusion. The fractal geometry is applied for unknown information modelling. Integrated techniques in computer graphics and computer vision are used. A new method is ...

A Geometria Fractal é um tema que tem sido pouco explorado nos ensinos fundamental e médio, apesar da sua extrema utilidade na descrição das formas construídas pela natureza. O objetivo geral desse trabalho foi propor analisar estratégias didáticas para ensinar a geometria fractal, no ensino partir observação dos objetos fenômenos naturais criados pelo homem. Apesar perfeita adequação propostas...

It has been ascertained that the human brain is a complex system studied at multiple scales, from neurons and microcircuits to macronetworks. The brain is characterized by a hierarchical organization that gives rise to its highly topological and functional complexity. Over the last decades, fractal geometry has been shown as a universal tool for the analysis and quantification of the geometric ...

Fractal geometry has been applied widely in the analysis of medical images to characterize the irregular complex tissue structures that do not lend themselves to straightforward analysis with traditional Euclidean geometry. In this study, we treat the nonfractal behaviour of medical images over large-scale ranges by considering their box-counting fractal dimension as a scale-dependent parameter...

Based on his earlier work on the vibrations of 'drums with fractal boundary', the first author has refined M. V. Berry's conjecture that extended from the 'smooth' to the 'fractal' case H. Weyl's conjecture for the asymptotics of the eigenvalues of the Laplacian on a bounded open subset of W (see [16]). We solve here in the one-dimensional case (that is, when n = 1) this 'modified Weyl-Berry co...

the soil water retention curve (swrc) is a basic characteristic of the determination of soil hydraulic properties, including unsaturated hydraulic conductivity. measurement of this curve is essential to research, thus scientists have focused on indirect methods such as pedotransfer functions and empirical relationships to estimate swrc easily. since there is a close relationship between swrc an...

Different summarized shape indices, like mean shape index (MSI) and area weighted mean shape index (AWMSI) can change over multiple size scales. This variation is important to describe scale heterogeneity of landscapes, but the exact mathematical form of the dependence is rarely known. In this paper, the use of fractal geometry (by the perimeter and area Hausdorff dimensions) made us able to de...

In this paper we describe a novel scheme for 2D shape representation based on fractal geometry. The representation (or fractal signature) of the shape is an external scalar transform which contains information from a wide range of scales. It appears to be unique except for size, orientation, position and reflection and we show that it degrades gracefully with noise. We show how the fractal sign...