ABSTRACT
In natural systems, there are many complex structures that cannot be described in terms of classic geometry and analysis. The Polish mathematician Benoit Mandelbrot is considered the father of Fractal Geometry. The Fractal Geometry and the concept of fractal dimension (FD) are of crucial importance for the characterization of complex nanostructures. The fractality of a protein surface manifests itself through distinctive global and local features of the surface roughness, resulting in dissimilar local and global fractal surface dimensions. The concept of FD was developed in mathematics, but it has applications in many other fields, from decorative art to science and technology. Fractal technology may lead to advances in photovoltaic electric generating systems, membranes for fuel cells or gas separation, soft-touch polymers, unique thermal properties, and high-resolution touch screens. Fractal nanostructures have been discovered on the surface of cancer cells.
