Mandelbrot introduced the concept of a fractal dimension, defined by adding 1 to the exponent of the power law (the value of the slopes). Thus the fractal dimension of the South African coast is 1.02, Norway 1.52, and so on. The point of adding the 1 was to connect the idea of fractals to the conventional concept of ordinary dimensions discussed in chapter 2. Recall that a smooth line has dimension 1, a smooth surface dimension 2, and a volume dimension
