Fractal art

The article considers various aspects of fractal art phenomenon, especially fractals in painting and literature. The works by B. Mandelbrot, which demonstrated the versatility of fractal geometry and raised the question of its aesthetic value, had a great influence on art and humanities studies. But in most cases, the term «fractal art» is used metaphorically. As a rule, these properties of fractals properties are taken for comparison: self-similarity, autoreference and possible infinity of iterations.
It should be noted that what changes is not the art itself, but the view of the researcher. The art critics and mathematicians discover «fractals before fractals» in the paintings by Wang ZiMeng, Leonardo da Vinci, Katsushika Hokusai – the artists who tried to display the incomprehensible beauty of the world, and, not knowing that, recreated the fractals. Rich material for the anticipation of the discovery of fractals is given in the works of the twentieth century artists, such as: Frantisek Kupka, Salvador Dali, Maurits Escher.
Particular attention is given to R. Taylor’s computer studies of Pollock’s abstract paintings, which showed permanence of fractal dimension D regardless the selected measurement scale in his canvases. As a result, «the fractal test» was proposed as a way to identify his paintings.
There described the «Fractal Art» ( in the literal sense), which started with the exhibition of fractal images organized by the researchers of the University of Bremen, headed by Heinz-Otto Peitgen and Michael M. Richter.
Continuing Yu. Stepanov’s and T. Bonch-Osmolovskaya’s researches, the authors examine the different types of «fractals» in literature. First of all, it is the structure «the text within the text», that, in some cases, has got a relatively self-similarity and autoreference and has created infinite meanings (as example the works by J.-L. Borges, V. Nabokov, M. Bulgakov, Yu. Trifonov are considered). Other example is the «crown of sonnets» in the poetry of Silver Age. The various functions of the fractal structure of texts are analyzed.