Understanding Fractal Analysis? The Case of Fractal Linguistics

Abstract

Terms such as ‘self-similarity’, ‘space filling’, ‘fractal dimension’, and associated concepts have different meanings to different people depending on their background. We examine how methodology in fractal analysis is influenced by diverse definitions of fundamental concepts that lead to difficulties in understanding fundamental issues. The meaning of terms associated with fractal analysis needs to be clarified if this method is to be useful in diverse disciplines. It is our premise that communications that are result focused constitute a danger in perpetuating misconceptions of terms due to the concise nature of the writing and the reliance on references to fill in the procedural and conceptual gaps. Communicating effectively requires a sound understanding of the terminology and a clear and meaningful presentation. We address here communication and the nature of scientific discourse, ‘fractal linguistics’.

Computational Analyses of Arteriovenous Malformations in Neuroimaging

“…] and Jelinek et al [Ref. ]). FD has also been investigated as a quantitative parameter of the 3‐dimensional geometrical complexity of the AVM.…”

Simple geometry in complex organisms

“…This observation may be of value in pre-clinical pathological diagnostics, and a correlation between these findings and tissue palpation would be useful research in the future. Fractal analysis is commonly applied to natural structures, where similar shapes and patterns appear at different size scales, linking hierarchies throughout the body (Mandelbrot, 1983;Skelton et al, 2001;Jelinek et al, 2006); the branching patterns of blood vessels, the bronchial tree and nerve fibres all display this property (Zamir, 2001;Palagyia et al, 2006;Phalen et al, 1978;Thomas et al, 2005). These characteristic shapes are developmental remnants of non-linear dynamic systems which were sensitive to small changes in the local environment, created instabilities in growth and caused the typical branching pattern which extends from the micro to the macro scale.…”

Fractal dimension and wavelet decomposition for robust microarray data clustering

“…Fractals and Wavelets have been used in numerous disciplines including bioinformatics [7][8][9]. For example, Fractal dimension (FD) based analysis of DNA strands showed that non-coding regions have a higher correlation and a higher range of self-similarity than exons (coding regions) [8].…”

“…For example, Fractal dimension (FD) based analysis of DNA strands showed that non-coding regions have a higher correlation and a higher range of self-similarity than exons (coding regions) [8]. The FD approach is based on characterization of the self similarity degree of a dataset to cluster points by making sure that none of the points belonging to a cluster changes the cluster's real dimension [9]. Self similarity means that an object is composed of multiple levels that statistically resemble the structure of the whole object.…”