ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


The 100th anniversary of fractal geometry: From Julia and Fatou through Hausdorff and Besicovitch to Mandelbrot

The purpose of this article is to present the biographies of the main creators of fractal geometry from the moment the first ideas arose, when the term «fractal» did not exist, to the present day. The main subjects of the article are Julia, Fatou, Richardson, Hausdorff, Besicovitch and Mandelbrot. The fates of these people are rich in dramatic events, some are tragic. Methods.

A brief review of the research results of new methods for generating, transmitting and receiving oscillations and waves based on fractal geometry methods

Purpose of this article is to generalize results of the application of fractal geometry methods in various radiophysic systems and at study of processes occurring in them. Methods. The presentation is built in the form of a brief review of a number of works devoted to new methods for generating, receiving and transmitting signals of various frequency ranges, including microwave frequencies, using fractal geometry approaches.

Self-­similarity at different scale levels in irradiated solid materials

Self-organized structures after ion-beam irradiation in solid materials have been studied using the method of fractal dimension. General computer method of the scale invariance evaluation for exposed dispersive structures is described. It was demonstrated that structures after irradiation can be characterized by the compatibility of scale invariance properties at different scale levels.

Fractal geometry

The article deals with the bases of fractal geometry and fates of its creators. The biographies and the discoveries of Felix Hausdorff and Abram Besicovitch – the main characters of the great play called fractal geometry – are presented with the possible degree of detail. There is no doubt that the author and director of this play was Benoit Mandelbrot. The article presents his biography and brief descriptions of the lives of his predecessors: Henri Poincare, Maurice Gaston Julia and Pierre Gaston Jose Fatou.