A fractal is a term used in geometry to describe an object the shape of which is intermediate between topological ideals. A fractal object is described by a fractal dimension. Such a parameter describes the deviation that a line, surface, or volume has from a topological ideal. For example, an ideal topological line has a dimension equal to 1, and an ideal plane has a topological dimension equal to 2.A fractal line, though, has a fractal dimension greater than 1, butless than 2, and a fractal surface has a fractal dimension greater than 2 but less than 3. As an experiment, the distance can be measured between two arbitrarily located points on a coastline. By using different rulers of progressively smaller sizes, the measured length will be found to increase as ruler size decreases. This epitomizes fractals. If the number of rulers required to travel between two points is called n and the ruler length is called y, then length l is equal to ny. For a fractal, the plot of log (n) versus log (y) yields a straight line; moreover, fractal dimension is equal to the absolute value of the slope of this line. Initial experiments show that circumferential traces of aggregate are fractal lines, witth dimensionsbetween 1 and 1.3. In general, greater fractal dimensions are foundfor rough, irregular aggregate. Fractal dimensions approach 1 for circumferential tracks of smooth, rounded pieces and for flat, elongated pieces. Lower fractal dimensions are also found for aggregate where shapes approach ideal, angular shapes, such as squares or triangles. The fractal dimension, therefore, appears promising for the characterization of aggregate. This paper appears in transportation research record no. 1278, Dynamic testing of aggregates and soils and lateral stress measurements 1990.
Abstract