分形几何Fractal Geometry(Ch1).ppt

Very roughly, a dimension provides a description of how much space a set fills. It is a measure of the prominence of the irregularities of a set when viewed at very small scales. When we refer to a set F as a fractal, therefore, we will typically have the following in mind. (i) F has a fine structure, i.e. detail on arbitrarily small scales. (ii) F is too irregular to be described in traditional geometrical language, both locally and globally. (iii) Often F has some form of self-similarity, perhaps approximate or statistical. (iv) Usually, the ‘fractal dimension’ of F (defined in som