11.  Fractals

11.1  Informal definitions

B. Mandelbrot (1975) coined the word "fractal" from the Latin word "fractus" meaning fragment. He introduced fractals as objects that are "apparently" complex, but in fact simply defined. A fractal object is such that :

(i) Its parts at all spatial scales are similar, strictly or approximately, to the object itself (or one of its parts);

(ii) It is extremely irregular at all spatial scales (p. 3 of ). A fractal object is infinitely fragmented (i.e. it has details at every spatial scale);

(iii) It contains...