Fractal art

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Hindu temples feature self-similar, fractal-like structures, where parts resemble the whole. Hindu Temple Design.jpg
Hindu temples feature self-similar, fractal-like structures, where parts resemble the whole.
Islamic geometric patterns are reminiscent of fractal art, as on the main dome of Selimiye Mosque in Edirne, Turkey, with self-similar patterns. Selimiye Mosque, Dome.jpg
Islamic geometric patterns are reminiscent of fractal art, as on the main dome of Selimiye Mosque in Edirne, Turkey, with self-similar patterns.

Fractal art is a form of algorithmic art created by calculating fractal objects and representing the calculation results as still digital images, animations, and media. Fractal art developed from the mid-1980s onwards. [2] It is a genre of computer art and digital art which are part of new media art. The mathematical beauty of fractals lies at the intersection of generative art and computer art. They combine to produce a type of abstract art.

Contents

Fractal art (especially in the western world) is rarely drawn or painted by hand. It is usually created indirectly with the assistance of fractal-generating software, iterating through three phases: setting parameters of appropriate fractal software; executing the possibly lengthy calculation; and evaluating the product. In some cases, other graphics programs are used to further modify the images produced. This is called post-processing. Non-fractal imagery may also be integrated into the artwork. [3] The Julia set and Mandelbrot sets can be considered as icons of fractal art. [4]

It was assumed that fractal art could not have developed without computers because of the calculative capabilities they provide. [5] Fractals are generated by applying iterative methods to solving non-linear equations or polynomial equations. Fractals are any of various extremely irregular curves or shapes for which any suitably chosen part is similar in shape to a given larger or smaller part when magnified or reduced to the same size. [6]

Types

A detail from a non-integer Multibrot set NonIntegerMultibrot - Breaking of Space.jpg
A detail from a non-integer Multibrot set

There are many different kinds of fractal images. They can be subdivided into several groups.

Fractal Expressionism is a term used to differentiate traditional visual art that incorporates fractal elements such as self-similarity for example. Perhaps the best example of fractal expressionism is found in Jackson Pollock's dripped patterns. They have been analysed and found to contain a fractal dimension which has been attributed to his technique. [9]

Techniques

Fractals of all kinds have been used as the basis for digital art and animation. High resolution color graphics became increasingly available at scientific research labs in the mid-1980s. Scientific forms of art, including fractal art, have developed separately from mainstream culture. [10] Starting with 2-dimensional details of fractals, such as the Mandelbrot Set, fractals have found artistic application in fields as varied as texture generation, plant growth simulation, and landscape generation.

Fractals are sometimes combined with evolutionary algorithms, either by iteratively choosing good-looking specimens in a set of random variations of a fractal artwork and producing new variations, to avoid dealing with cumbersome or unpredictable parameters, or collectively, as in the Electric Sheep project, where people use fractal flames rendered with distributed computing as their screensaver and "rate" the flame they are viewing, influencing the server, which reduces the traits of the undesirables, and increases those of the desirables to produce a computer-generated, community-created piece of art.

Many fractal images are admired because of their perceived harmony. This is typically achieved by the patterns which emerge from the balance of order and chaos. Similar qualities have been described in Chinese painting and miniature trees and rockeries. [11]

Landscapes

A 3D landscape generated with Terragen, using the Mandelbrot set Mandelbrot island.jpg
A 3D landscape generated with Terragen, using the Mandelbrot set

The first fractal image that was intended to be a work of art was probably the famous one on the cover of Scientific American , August 1985. This image showed a landscape formed from the potential function on the domain outside the (usual) Mandelbrot set. However, as the potential function grows fast near the boundary of the Mandelbrot set, it was necessary for the creator to let the landscape grow downwards, so that it looked as if the Mandelbrot set was a plateau atop a mountain with steep sides. The same technique was used a year after in some images in The Beauty of Fractals by Heinz-Otto Peitgen and Michael M. Richter. They provide a formula to estimate the distance from a point outside the Mandelbrot set to the boundary of the Mandelbrot set (and a similar formula for the Julia sets). Landscapes can, for example, be formed from the distance function for a family of iterations of the form .

Artists

Notable fractal artists include Desmond Paul Henry, Hamid Naderi Yeganeh, and musician Bruno Degazio. British artists include William Latham, who has used fractal geometry and other computer graphics techniques in his works. [12] and Vienna Forrester who creates flame fractal art using data extracted from her photographs. Greg Sams has used fractal designs in postcards, T-shirts, and textiles. American Vicky Brago-Mitchell has created fractal art which has appeared in exhibitions and on magazine covers. Scott Draves is credited with inventing flame fractals. Carlos Ginzburg has explored fractal art and developed a concept called "homo fractalus" which is based around the idea that the human is the ultimate fractal. [13] Merrin Parkers from New Zealand specialises in fractal art. [14] Kerry Mitchell wrote a "Fractal Art Manifesto", claiming that. [15] In Italy, the artist Giorgio Orefice wrote the "Fractalism" manifesto, founding a Fractalism cultural mouvement in 1999. [16]

Fractal Art is a subclass of two-dimensional visual art, and is in many respects similar to photography—another art form that was greeted by skepticism upon its arrival. Fractal images typically are manifested as prints, bringing fractal artists into the company of painters, photographers, and printmakers. Fractals exist natively as electronic images. This is a format that traditional visual artists are quickly embracing, bringing them into Fractal Art's digital realm. Generating fractals can be an artistic endeavor, a mathematical pursuit, or just a soothing diversion. However, Fractal Art is clearly distinguished from other digital activities by what it is, and by what it is not. [15]

According to Mitchell, fractal art is not computerized art, lacking in rules, unpredictable, nor something that any person with access to a computer can do well. Instead, fractal art is expressive, creative, and requires input, effort, and intelligence. Most importantly, "fractal art is simply that which is created by Fractal Artists: ART." [15]

American artist Hal Tenny was hired to design environment in the 2017 film Guardians of the Galaxy Vol. 2 . [17] There has also been a surge in fractal art distributed via Non-fungible tokens - such as work listed by Fractal_Dimensions, spectral.haus, and NetMetropolis. [18]

Exhibits

Fractal art exhibition, 2013 Burst Fractal Art Show.jpg
Fractal art exhibition, 2013

Fractal art has been exhibited at major international art galleries. [19] One of the first exhibitions of fractal art was "Map Art", a travelling exhibition of works from researchers at the University of Bremen. [20] Mathematicians Heinz-Otto Peitgen and Michael M. Richter discovered that the public not only found the images aesthetically pleasing but that they also wanted to understand the scientific background to the images. [21]

In 1989, fractals were part of the subject matter for an art show called Strange Attractors: Signs of Chaos at the New Museum of Contemporary Art. [10] The show consisted of photographs, installations and sculptures designed to provide greater scientific discourse to the field which had already captured the public's attention through colourful and intricate computer imagery.

In 2014, emerging British fractal artist Vienna Forrester [22] created an exhibition held at the I-node of the Planetary Collegium, [23] Kefalonia, entitled "IO. Fragmented Myths and Memories: A Fractal Exploration of Kefalonia", [24] part of the 2013–14 international arts festival "Stone Kingdom Kefalonia" commemorating the devastating 1953 Ionian earthquake. [23] Her works were created by using geographical coordinates and photographs from parts of the island which still bear the scars.

Artworks

"Global Forest" [25] artwork is based on a study highlighting the aesthetic and physiological impacts of fractal patterns. Fractals, patterns found universally in nature, repeat self-similarly across scales, with the complexity and aesthetic perception determined by their recursion and dimension rate. Notably, these patterns are featured in art across various cultures, including Jackson Pollock's paintings, eliciting strong aesthetic reactions. Moreover, incorporating fractals in architectural designs can mitigate visual strain and discomfort caused by Euclidean spaces and even reduce stress, resonating with the biophilic idea of humans' innate connection to nature. The ScienceDesignLab collaborated with the Mohawk Group to integrate these findings, producing award-winning "Relaxing Floors" that use fractal patterns, hypothesizing their therapeutic effects stem from nature's soothing visuals.

See also

Related Research Articles

<span class="mw-page-title-main">Benoit Mandelbrot</span> French-American mathematician (1924–2010)

Benoit B.Mandelbrot was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature.

<span class="mw-page-title-main">Fractal</span> Infinitely detailed mathematical structure

In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar. Fractal geometry lies within the mathematical branch of measure theory.

<span class="mw-page-title-main">Mandelbrot set</span> Fractal named after mathematician Benoit Mandelbrot

The Mandelbrot set is a two-dimensional set with a relatively simple definition that exhibits great complexity, especially as it is magnified. It is popular for its aesthetic appeal and fractal structures. The set is defined in the complex plane as the complex numbers for which the function does not diverge to infinity when iterated starting at , i.e., for which the sequence , , etc., remains bounded in absolute value.

<span class="mw-page-title-main">Self-similarity</span> Whole of an object being mathematically similar to part of itself

In mathematics, a self-similar object is exactly or approximately similar to a part of itself. Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape. The non-trivial similarity evident in fractals is distinguished by their fine structure, or detail on arbitrarily small scales. As a counterexample, whereas any portion of a straight line may resemble the whole, further detail is not revealed.

<span class="mw-page-title-main">Sierpiński triangle</span> Fractal composed of triangles

The Sierpiński triangle, also called the Sierpiński gasket or Sierpiński sieve, is a fractal attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. Originally constructed as a curve, this is one of the basic examples of self-similar sets—that is, it is a mathematically generated pattern that is reproducible at any magnification or reduction. It is named after the Polish mathematician Wacław Sierpiński, but appeared as a decorative pattern many centuries before the work of Sierpiński.

<span class="mw-page-title-main">Fractal landscape</span> Stochastically generated naturalistic terrain

A fractal landscape or fractal surface is generated using a stochastic algorithm designed to produce fractal behavior that mimics the appearance of natural terrain. In other words, the surface resulting from the procedure is not a deterministic, but rather a random surface that exhibits fractal behavior.

<span class="mw-page-title-main">Clifford A. Pickover</span> American inventor and author (b. 1957)

Clifford Alan Pickover is an American author, editor, and columnist in the fields of science, mathematics, science fiction, innovation, and creativity. For many years, he was employed at the IBM Thomas J. Watson Research Center in Yorktown, New York, where he was editor-in-chief of the IBM Journal of Research and Development. He has been granted more than 700 U.S. patents, is an elected Fellow for the Committee for Skeptical Inquiry, and is author of more than 50 books, translated into more than a dozen languages.

In mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the scale at which it is measured. It is also a measure of the space-filling capacity of a pattern, and it tells how a fractal scales differently, in a fractal (non-integer) dimension.

<span class="mw-page-title-main">Iterated function system</span> Method for the construction of fractals

In mathematics, iterated function systems (IFSs) are a method of constructing fractals; the resulting fractals are often self-similar. IFS fractals are more related to set theory than fractal geometry. They were introduced in 1981.

<span class="mw-page-title-main">Buddhabrot</span> Probability distribution over the trajectories of points that escape the Mandelbrot fractal

The Buddhabrot is the probability distribution over the trajectories of points that escape the Mandelbrot fractal. Its name reflects its pareidolic resemblance to classical depictions of Gautama Buddha, seated in a meditation pose with a forehead mark (tikka), a traditional oval crown (ushnisha), and ringlet of hair.

<span class="mw-page-title-main">Pickover stalk</span> Inherent structure of the mandelbrot set

Pickover stalks are certain kinds of details to be found empirically in the Mandelbrot set, in the study of fractal geometry. They are so named after the researcher Clifford Pickover, whose "epsilon cross" method was instrumental in their discovery. An "epsilon cross" is a cross-shaped orbit trap.

<span class="mw-page-title-main">Burning Ship fractal</span> Complex plane fractal

The Burning Ship fractal, first described and created by Michael Michelitsch and Otto E. Rössler in 1992, is generated by iterating the function:

<span class="mw-page-title-main">Algorithmic art</span> Art genre

Algorithmic art or algorithm art is art, mostly visual art, in which the design is generated by an algorithm. Algorithmic artists are sometimes called algorists.

<span class="mw-page-title-main">Desmond Paul Henry</span> British philosopher

Desmond Paul Henry (1921–2004) was a Manchester University Lecturer and Reader in Philosophy (1949–82). He was one of the first British artists to experiment with machine-generated visual effects at the time of the emerging global computer art movement of the 1960s. During this period, Henry constructed a succession of three electro-mechanical drawing machines from modified bombsight analogue computers which were employed in World War II bombers to calculate the accurate release of bombs onto their targets. Henry's machine-generated effects resemble complex versions of the abstract, curvilinear graphics which accompany Microsoft's Windows Media Player. Henry's machine-generated effects may therefore also be said to represent early examples of computer graphics: "the making of line drawings with the aid of computers and drawing machines".

<i>The Beauty of Fractals</i> Book by Heinz-Otto Peitgen

The Beauty of Fractals is a 1986 book by Heinz-Otto Peitgen and Peter Richter which publicises the fields of complex dynamics, chaos theory and the concept of fractals. It is lavishly illustrated and as a mathematics book became an unusual success.

<span class="mw-page-title-main">Fractal-generating software</span>

Fractal-generating software is any type of graphics software that generates images of fractals. There are many fractal generating programs available, both free and commercial. Mobile apps are available to play or tinker with fractals. Some programmers create fractal software for themselves because of the novelty and because of the challenge in understanding the related mathematics. The generation of fractals has led to some very large problems for pure mathematics.

<span class="mw-page-title-main">Orbit trap</span> Method of colouring fractal images

In mathematics, an orbit trap is a method of colouring fractal images based upon how close an iterative function, used to create the fractal, approaches a geometric shape, called a "trap". Typical traps are points, lines, circles, flower shapes and even raster images. Orbit traps are typically used to colour two dimensional fractals representing the complex plane.

<span class="mw-page-title-main">Mandelbox</span> Fractal with a boxlike shape

In mathematics, the mandelbox is a fractal with a boxlike shape found by Tom Lowe in 2010. It is defined in a similar way to the famous Mandelbrot set as the values of a parameter such that the origin does not escape to infinity under iteration of certain geometrical transformations. The mandelbox is defined as a map of continuous Julia sets, but, unlike the Mandelbrot set, can be defined in any number of dimensions. It is typically drawn in three dimensions for illustrative purposes.

Kerry Mitchell is an American artist known for his algorithmic and fractal art, which has been exhibited at the Nature in Art Museum, The Bridges Conference, and the Los Angeles Center for Digital Art, and for his "Fractal Art Manifesto".

Fractal expressionism is used to distinguish fractal art generated directly by artists from fractal art generated using mathematics and/or computers. Fractals are patterns that repeat at increasingly fine scales and are prevalent in natural scenery. Fractal expressionism implies a direct expression of nature's patterns in an art work.

References

  1. ↑ Trivedi, K. (1989). "Hindu Temples: Models of a Fractal Universe". The Visual Computer. 5 (4): 243–258. doi:10.1007/BF02153753. S2CID   29185088.
  2. ↑ Bovill, Carl (1996). Fractal geometry in architecture and design. Boston: Birkhauser. p. 153. ISBN   0-8176-3795-8 . Retrieved October 28, 2011.
  3. ↑ Elysia Conner (February 25, 2009). "Meet Reginald Atkins, mathematical artist". CasperJournal.com. Archived from the original on April 20, 2012. Retrieved October 28, 2011.
  4. ↑ Burger, Edward B.; Michael P. Starbird (2005). The heart of mathematics: an invitation to effective thinking. Springer. p. 475. ISBN   1-931914-41-9 . Retrieved October 30, 2011.
  5. ↑ Steven R., Holtzman (1995). Digital Mantras: The languages of abstract and virtual worlds. MIT Press. p. 241. ISBN   0-262-58143-4 . Retrieved October 28, 2011.
  6. ↑ Fractal – Definition. Free Merriam-Webster Dictionary.
  7. ↑ "Quaternion Julia Fractals".
  8. ↑ "Fractal Art FAQ".
  9. ↑ Érdi, Péter (2008). Complexity explained. Springer. p. 214. ISBN   978-3-540-35777-3 . Retrieved October 29, 2011.
  10. 1 2 Penny, Simon (1995). Critical issues in electronic media. State University of New York Press. pp. 81–82. ISBN   0-7914-2317-4 . Retrieved October 29, 2011.
  11. ↑ Wang, Hongyu (2005). "Chinese aesthetics, Fractals and the Tao of Curriculum". In Doll, Jr, William E.; Fleener, Jayne; Trueit, Donna; et al. (eds.). Chaos, complexity, curriculum and culture. New York: Peter Lang Publishing. p. 301. ISBN   978-0-8204-6780-1 . Retrieved October 28, 2011.
  12. ↑ Briggs, John (1992). Fractals: The Patterns of Chaos. London: Thames and Hudson. p. 169. ISBN   0-500-27693-5.
  13. ↑ "Carlos Ginzburg". Leonardo . Leonardo/ISAST, the International Society for the Arts, Sciences and Technology. 2001. Retrieved October 29, 2011.
  14. ↑ Jackson, William Joseph (2004). Heaven's fractal net: retrieving lost visions in the humanities, Volume 1. Indiana University Press. p. 116. ISBN   0-253-21620-6 . Retrieved October 30, 2011.
  15. 1 2 3 Mitchell, Kerry. "The Fractal Art Manifesto" . Retrieved December 28, 2015.
  16. ↑ "Inaugurata la biennale d'arte contemporanea". Digitale terrestre free: canale 652 (in Italian). April 17, 2019. Retrieved November 11, 2021.
  17. ↑ Giardina, Carolyn (May 8, 2017). "'Guardians of the Galaxy Vol. 2': A Digital Kurt Russell and Other VFX Tricks Revealed". The Hollywood Reporter . Archived from the original on May 15, 2017. Retrieved September 29, 2023.
  18. ↑ "Mandelbrot Set Collection | OpenSea" . Retrieved April 24, 2022.
  19. ↑ Barrow, John D. (1995). The artful universe expanded. Oxford University Press. p. 69. ISBN   0-19-280569-X . Retrieved October 28, 2011.
  20. ↑ Robertson, George (1996). FutureNatural. London: Routledge. pp. 220–221. ISBN   0-415-07013-9 . Retrieved October 28, 2011.
  21. ↑ Richard Wright. "Art and Science in Chaos: Contesting Readings of Scientific Visualisation". ISEA'94 Proceedings – The Next Generation. University of Iowa. Archived from the original on October 1, 2011. Retrieved October 28, 2011.
  22. ↑ "Vienna Forrester - Fractal Artist". viennaforrester.art. Retrieved June 17, 2021.
  23. 1 2 "Fractal Art – Research – Fine Art Studies". Reece Hill at De Montfort University Leicester. November 6, 2020. Archived from the original on October 28, 2023. Retrieved September 29, 2023.
  24. ↑ "VIENNA FORRESTER: Fragmented Myths and Memories". Ionion Center for the Arts and Culture. October 25, 2014. Retrieved June 17, 2021. ...Stone Kingdom that is the beautiful island of Kefalonia.
  25. ↑ Robles, Kelly E.; Roberts, Michelle; Viengkham, Catherine; Smith, Julian H.; Rowland, Conor; Moslehi, Saba; Stadlober, Sabrina; Lesjak, Anastasija; Lesjak, Martin; Taylor, Richard P.; Spehar, Branka; Sereno, Margaret E. (August 17, 2021). "Aesthetics and Psychological Effects of Fractal Based Design". Frontiers in Psychology. 12. doi: 10.3389/fpsyg.2021.699962 . ISSN   1664-1078. PMC   8416160 . PMID   34484047.

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