Fractal Geometry: Historical and Conceptual Background

Presently, fractal geometry serves as a framework for studies of complex systems of diverse nature. One of the most fundamental geometric conceptions is the concept of symmetry. Different geometries can be classified according to the group of transformations under which their propositions remain true. In particular, the key symmetries of the fractal geometry are the 5 scale and conformal invariance. Another key paradigm in the fractal geometry is that different properties of a fractal pattern are associated with different dimension numbers, at least one of which differs fromthe topological dimension. Accordingly, the inherent features of a fractal pattern are characterized by a set of generally independent dimension numbers. These numbers allow for the classification of fractal patterns. In this review we briefly survey the historical background and the conceptual foundations of fractal geometry.