Journal of Food, Agriculture and Environment

Vol 1, Issue 2,2003
Online ISSN: 1459-0263
Print ISSN: 1459-0255

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


D. L. Critten

Recieved Date: 2003-01-12, Accepted Date: 2003-04-27


We first describe experiments designed to obtain fractal dimensions (dk) 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 (dk). We find plausible values of between 1 and 3 for space-filled vector dimensions (n) that correspond to the measured fractal dimensions (dk). 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 (dk) obtained using (L) agree well with those obtained from the defining bijection equation.


Plant, canopy, patterns, measurements

Journal: Journal of Food, Agriculture and Environment
Year: 2003
Volume: 1
Issue: 2
Category: Agriculture
Pages: 238-243

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