An Analysis of space-filling fractal dimensions, resulting from measurements on plant canopies

Author: D. L. Critten

Received 12 January 2003, accepted 27 April 2003.

Abstract

We first describe experiments designed to obtain fractal dimensions (d_k) associated with different plant canopies. The method involves 2 or 3-dimensional Fourier analyses of grey levels within photographic or video images of square sections of the canopy, viewed vertically downwards. From these analyses amplitude/ wavenumber relationships are used to obtain fractal dimensions (d_k). We find plausible values of between 1 and 3 for space-filled vector dimensions (n) that correspond to the measured fractal dimensions (d_k). A linear relationship between the exponent (σ) from the amplitude/wavenumber relationship and vector dimensions (n) is discovered. This relationship is shown not to match the non-linear (bijection) equation which defines (n). A theory which brings these results into concord is then presented, generating a correction factor (L) for the linear relationship. The factor recognises the restriction of ‘information’ which must occur when a single defining vector dimension is used to represent isotropic patterns from 2 or more vector dimensions. Agreement between predicted values of (L) and values gleaned from the literature is broadly satisfactory, and synthesised values of (d_k) obtained using (L) agree well with those obtained from the defining bijection equation.

Journal: Food, Agriculture & Environment (JFAE)
Online ISSN: 1459-0263
Year: 2003, Vol. 1, Issue 2, pages 238-243.
Publisher: WFL