**fractal structure**(rus. фрактальная структура) — (from Latin

*fractus*meaning broken, uneven, past participle of frangere to break) a structure that is characterised with self-similarity, i.е. it is composed of such fragments whose structural motif is repeated if the scale changes.

### Description

The fractal structure is described as the degree of occupancy of a structure in a space (dimension), which is not an integer value. Thus, n-dimensional fractals occupy an intermediate position between the n-dimensional and (n + 1)-dimensional objects. To construct a regular fractal object, recursive functions are used.

In natural fractal-like structures, there is no fractional dimension and self-similarity is observed only up to a certain scale, as opposed to regular fractals. Examples of natural objects with a fractal-like structure are cumulus clouds, trees, lightning. For example, in the crown each of the big tree branches is divided into at least two smaller branches, and then the branches divide again and again (see Fig.). As a result, each branch can be considered as a single repeating motive of a fractal structure.

The geometry of some of nanosystems, such as dendrimer molecules and fractal clusters is accurately described with recursive functions enabling the simulation of their micro-and macroscopic properties.

In natural fractal-like structures, there is no fractional dimension and self-similarity is observed only up to a certain scale, as opposed to regular fractals. Examples of natural objects with a fractal-like structure are cumulus clouds, trees, lightning. For example, in the crown each of the big tree branches is divided into at least two smaller branches, and then the branches divide again and again (see Fig.). As a result, each branch can be considered as a single repeating motive of a fractal structure.

The geometry of some of nanosystems, such as dendrimer molecules and fractal clusters is accurately described with recursive functions enabling the simulation of their micro-and macroscopic properties.

### Illustrations

#### Authors

- Shlyakhtin Oleg A.
- Streletskiy Alexey V.

#### Sources

- Feder J. Fractals (Physics of Solids and Liquids). — Springer, 1988. — 310 pp.
- Tret'jakov Ju. D. Dendrites, Fractals and Materials (in Russian). // Sorosovskijj obrazovatel'nyjj zhurnal. 1998. №11. 96–102 pp.
- Peitgen H.-O., Richter P. H. The Beauty of Fractals: Images of Complex Dynamical Systems. — Springer-Verlag, 1987. — 199 pp.