Fractals Everywhere

This book is based on a course called 'Fractal Geometry' which has been taught in the School of Mathematics at Georgia Institute of Technology for two years. 'Fractals Everywhere' teaches the tools, methods, and theory of deterministic geometry. Ti is useful for describing specific objects and structures. Models are represented by succinct 'formulas.' Once the formula is known, the model can be reproduced. we do not consider statistical geometry. The latter aims at discovering general statistical laws which govern families of similar-looking structures, such as all cumulus clouds, all maple leaves, or all mountains. In deterministic geometry, structures are defined, communicated, and analysed, with the aid of elementary transformations such as affine transformations, scalings, rotations, and congruences. A fractal set generally contains infinitely many points whose organization is so complicated that it is not possible to describe the set by specifying directly where each point in it lies. Instead, the set may be define by 'the relations between the pieces.' It is rather like describing the solar system by quoting the law of gravitation and stating the initial conditions. Everything follows from that. It appears always to be better to describe in terms of relationships.