Fractals and Spatial Geometry - An Application to Veins in the Otago Schist

Most people are familiar with Euclidean dimensions: zero for a point; one for a line; two for a plane; and three for a volume. Howeverbobjects are not actually Euclidean, but lie somewhere between Euclidean æend-membersÆ with a non-integer fractal (or æfractionalÆ) dimension. The fractal dimension D is a measure of the relative importance of large versus small. Consider the trace of a coastline on a map. It has a fractal dimension (1 =D =2) somewhere between a line (dimension = 1) and a plane (dimension = 2). The more tortuous the coastline, the higher the fractal dimension, and the closer it becomes towards a plane. The concepts of fractals and spatial geometry can be applied to a wide range of geologicaVmining problems as well as than those dealing with space. One commonly quoted fractal relation is the log-log relationship of ore-grade and tonnage. Until recently, we have never been able to define or measure spatial-geometry, but new developments in mathematics have provided a means by which to quantity and apply it to our problems.