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Characterizing Fractal and Hierarchical Morphologies Beyond the Fractal Dimension

Published online by Cambridge University Press:  03 September 2012

Raphael Blumenfeld  and
Robin C. Ball
Raphael Blumenfeld
Affiliation:
CNLS and the Theoretical Division, MS B258, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Robin C. Ball
Affiliation:
Cavendish Laboratory, Madingley Road, Cambridge CB3 OHE, UK
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Abstract

We present a novel correlation scheme to characterize the morphology of fractal and hierarchical patterns beyond traditional scaling. The method consists of analysing correlations between more than two-points in logarithmic coordinates. This technique has several advantages: i) It can be used to quantify the currently vague concept of morphology; ii) It allows to distinguish between different signatures of structures with similar fractal dimension but different morphologies already for relatively small systems; iii) The method is sensitive to oscillations in logarithmic coordinates, which are both admissible solutions for renormalization equations and which appear in many branching patterns (e.g., noise-reduced diffusion-limited-aggregation and bronchial structures); iv) The methods yields information on corrections to scaling from the asymptotic behavior, which is very useful in finite size analysis. Markovian processes are calculated exactly and several structures are analyzed by this method to demonstrate its advantages.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 367: Symposium P – Fractal Aspects of Materials , 1994 , 367
Copyright
Copyright © Materials Research Society 1995

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