FRACTAL ART
Cite this article as:
Trubetskov D. I., Trubetskova E. G. FRACTAL ART. Izvestiya VUZ. Applied Nonlinear Dynamics, 2016, vol. 24, iss. 6, pp. 84-102. DOI: https://doi.org/10.18500/0869-6632-2016-24-6-84-102
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.
DOI: 10.18500/0869-6632-2016-24-6-84-102
Paper reference: Trubetskov D.I., Trubetscova E.G. Fractal art. Izvestiya VUZ. Applied Nonlinear Dynamics. 2016. Vol. 24. Issue 6. P. 84–102.
1. Danilov Yu.A. A Wonderful world of science. Coll. of articles dedicated to the memory of Yu.A. Danilov. Eds V.I. Sanyuk, D.I. Trubetskov. M.: Progress-Tradition, 2008. 384 p. (in Russian).
2. Art-fractal. Coll. articles. S-Pb: Strata, 2015. 156 p. (in Russian).
3. Demenok S. Superfraktal. S-Pb.: Strata. 2015. 191 p. (in Russian).
4. Mandelbrot B. The Fractal Geometry of Nature. Henry Holt and Company, 1982. 468 p.
5. Abraham R. Chaos and Fractals of Paris. In: Art-fractal. Coll. articles. S-Pb: Strata, 2015. P. 71–77. (in Russian).
6. Kocich L. Aartistic Elements of Fractal Structures. In: Art-fractal. Coll. articles. S-Pb: Strata, 2015. P. 78–97. (in Russian).
7. The World of M.C. Escher. Ed. J.L. Locher. N.Y.: Abradale Press. 1988.
8. Taylor R.P. Skillful chaos. Scientific American. 2003. N4. P. 70–75.
9. Taylor R.P., Micolich A.P., Jonas D. Fractal analysis of Pollock’s drip paintings. Nature. 1999. N 399.
10. Taylor R.P., Micolich A.P., Jonas D. Fractal Expressionism. Can Science be Used to Further our Understanding of Art? Physics World. 1999. N12. P. 25–28.
11. Taylor R.P. Splashdown. New Scientist. 1998. Vol. 159. P. 30–31.
12. Trinton D. Ordered and Chaotic Motion of a Forced Spherical Pendulum. European Journal of Physics. 1986. N7. Р. 162.
13. Peitgen P.O., Richter P.H. The Beauty of Fractals: Images of Complex Dynamical Systems. Springer-Verlag. 1986.
14. Eilenberger V. Freedom, Science and Aesthetics. In: Peitgen P.O., Richter P.H. The Beauty of Fractals: Images of Complex Dynamical Systems. Springer-Verlag. 1986. P. 175–180
15. Franke H.V. Refractions of Science into Art. In: Peitgen P.O., Richter P.H. The Beauty of Fractals: Images of Complex Dynamical Systems. Springer-Verlag. 1986. P. 181–187.
16. Fractal Art Manifest. Coll. articles. S-Pb: Strata, 2015. 156 p. (in Russian).
17. Bonch-Osmolovskaya T.V. Fractals in literature. http://www.ashtray.ru/main/texts/experlit/fractallit3.htm (in Russian).
18. Borges J.L. The Circular Ruins. In: Borges J.L. The Circular Ruins. Labyrinths: Selected Stories and Other Writings. New Directions. 1964. P. 45–50.
19. Nabokov V. The Gift .Vintage international, 1991. 344 p.
20. Marshak S. The House That Jack Built. M.: Detskaya Literatura. 1986. 52 р. (in Russian).
21. Voloshin M. Collected works in 10 v. V. 1. M.: Ellis Luck, 2003. (in Russian).
22. Porter L.G. Symmetry – Mistress of Poetry: an Essay on Beginning of General Theory of Poetic Structures. M.: Languages of Slavonic culture, 2003. (in Russian).
23. Trifonov Yu’. The Disappearance. Time and place. The Old Man. M.: Contemporary. 1989. (in Russian).
24. Meyrink G. The Golem. SPb.: Azbuka-klassica. 2004. (in Russian).
25. Lermontov M. Collected works in 10 v. Vol. 1. M.: Pravda, 1969. (in Russian).
26. Stepanov Yu. Proteus: Essays on chaotic evolution. M.: Languages of Slavic culture, 2004. (in Russian).
27. Nabokov about Nabokov and other things: Interviews, reviews, essays. Composed and commented by N. Melnikov. М.: Independent newspaper, 2002. P. 117–128. (in Russian).
28. Tarasenko V. Fractal logic. M.: Progress-Tradition, 2002. 155 p.(in Russian).
29. Tarasenko V. Fractal semiotics: «Blind Spots», Vicissitudes and Recognition. M.: Book House «LIBROKOM», 2012. 312 p. (in Russian).
30. Gospozha Udacha (Lady Luck). 1999. No 3. (in Russian).
BibTeX
author = {Dmitry Ivanovich Trubetskov and Elena Gennadjevna Trubetskova},
title = {FRACTAL ART},
year = {2016},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {24},number = {6},
url = {https://old-andjournal.sgu.ru/en/articles/fractal-art},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2016-24-6-84-102},pages = {84--102},issn = {0869-6632},
keywords = {Fractal art,fractals in the painting,fractals in the literature. M. Esher,J-L. Borges,V. Nabokov.},
abstract = { 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. DOI: 10.18500/0869-6632-2016-24-6-84-102 Paper reference: Trubetskov D.I., Trubetscova E.G. Fractal art. Izvestiya VUZ. Applied Nonlinear Dynamics. 2016. Vol. 24. Issue 6. P. 84–102. Download full version }}