Fractal geometry in forestry applications

Abstract

Fractal geometry can be used to describe length, surface, and volume of natural objects such as trees, rivers, and mountains. Unlike the straight lines of classical geometry, natural lines do not have unique invariable lenghts. They become longer when we use smaller units of measurement which are able to reveal finer details of the line. Although both unit and length change, the parameter governing these changes remains invariant. This parameter, called the fractal dimension, is specific for each line. Fractal dimensions of natural lines are greater than one and the excess indicates the degree of convolution. Not all tree variables are fractals. Stem surface is fractal, but volume is not. Therefore, volume as well as tree height should be calculated using the methods of classical geometry. At the same time, potential applications of fractal geometry are not limited to quantifying natural lines and surfaces. Fractal geometry may produce new methods for estimating stand density, predicting forest succession, and describing the form of trees. It is shown that the fractal dimension of tree crowns is a good indicator of various tree and site features such as species tolerance, crown class, and site quality. Therefore, the crown fractal dimension could be the most meaningful single number for tree description. At the same time, improved video cameras could make this dimension the easiest tree variable to measure.