The Fractal Dimension
Carl Bovill · Birkhäuser Boston eBooks · 1996
Each stage of the generation process for a fractal curve adds more length to the curve. A fractal curve generated through an infinite number of steps will have infinite length. It was demonstrated in Chapter 2 that the length of different fractal curves grows from one generation stage to the next at different rates. The rate of growth of the length of the fractal curve is the distinguishing feature of the curve. The central concept is that length and the size of the instrument used to measure it are related. The relationship turns out to be a power law (Mandelbrot, 1983): (y) is proportional to (x) d (3.1) These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.