Editing Fractal (section)

===In creative works===
{{Further|Fractal art|Mathematics and art}}

Since 1999 numerous scientific groups have performed fractal analysis on over 50 paintings created by [[Jackson Pollock]] by pouring paint directly onto horizontal canvasses.<ref>{{cite journal |first=R. P. |last=Taylor |display-authors=et al |title=Fractal Analysis of Pollock's Drip Paintings |journal=Nature |volume=399 |issue=6735 |page=422 |year=1999|bibcode=1999Natur.399..422T |doi=10.1038/20833 |s2cid=204993516 |doi-access=free }}</ref><ref>{{cite journal |first1=R. P. |last1=Taylor |display-authors=etal |title=Fractal Analysis: Revisiting Pollock's Paintings (Reply)|journal=Nature |volume=444 |issue=7119 |pages=E10–11 |year=2006 |doi=10.1038/nature05399|bibcode=2006Natur.444E..10T |s2cid=31353634 }}</ref><ref>{{cite journal |first1=S. |last1=Lee |first2=S. |last2=Olsen |first3=B. |last3=Gooch |title=Simulating and Analyzing Jackson Pollock's Paintings |journal=Journal of Mathematics and the Arts |volume=1 |issue=2 |pages=73–83 |year=2007 |doi=10.1080/17513470701451253|citeseerx=10.1.1.141.7470 |s2cid=8529592 }}</ref>

Recently, fractal analysis has been used to achieve a 93% success rate in distinguishing real from imitation Pollocks.<ref>{{cite journal |first1=L. |last1=Shamar |title=What Makes a Pollock Pollock: A Machine Vision Approach |journal=International Journal of Arts and Technology |volume=8 |pages=1–10 |year=2015 |doi=10.1504/IJART.2015.067389 |url=http://vfacstaff.ltu.edu/lshamir/publications/wm_pollock.pdf |citeseerx=10.1.1.647.365 |access-date=October 24, 2017 |archive-date=October 25, 2017 |archive-url=https://web.archive.org/web/20171025022609/http://vfacstaff.ltu.edu/lshamir/publications/wm_pollock.pdf |url-status=dead }}</ref> Cognitive neuroscientists have shown that Pollock's fractals induce the same stress-reduction in observers as computer-generated fractals and Nature's fractals.<ref>{{cite journal |first1=R. P. |last1=Taylor |first2=B. |last2=Spehar |first3=P. |last3=Van Donkelaar |first4=C. M. |last4=Hagerhall |title=Perceptual and Physiological Responses to Jackson Pollock's Fractals |journal=Frontiers in Human Neuroscience |volume=5 |pages=1–13 |year=2011 |doi=10.3389/fnhum.2011.00060|pmid=21734876 |pmc=3124832 |doi-access=free }}</ref>

[[Decalcomania]], a technique used by artists such as [[Max Ernst]], can produce fractal-like patterns.<ref>Frame, Michael; and Mandelbrot, Benoît B.; [http://classes.yale.edu/Fractals/Panorama/ ''A Panorama of Fractals and Their Uses''] {{Webarchive|url=https://web.archive.org/web/20071223090421/http://classes.yale.edu/Fractals/Panorama/ |date=December 23, 2007 }}</ref> It involves pressing paint between two surfaces and pulling them apart.

Cyberneticist [[Ron Eglash]] has suggested that fractal geometry and mathematics are prevalent in [[African art]], games, [[divination]], trade, and architecture. Circular houses appear in circles of circles, rectangular houses in rectangles of rectangles, and so on. Such scaling patterns can also be found in African textiles, sculpture, and even cornrow hairstyles.<ref name="African art">{{cite web |url=http://www.rpi.edu/~eglash/eglash.dir/afractal/afractal.htm |first=Ron |last=Eglash |title=African Fractals: Modern Computing and Indigenous Design |location=New Brunswick |publisher=Rutgers University Press |year=1999 |access-date=October 17, 2010 |archive-url=https://web.archive.org/web/20180103005701/http://homepages.rpi.edu/~eglash/eglash.dir/afractal/afbook.htm |archive-date=January 3, 2018 |url-status=dead }}</ref><ref>{{Cite web|last=Nelson|first=Bryn|date=2000-02-23|title=Sophisticated Mathematics Behind African Village Designs / Fractal patterns use repetition on large, small scale|url=https://www.sfgate.com/education/article/Sophisticated-Mathematics-Behind-African-Village-2774181.php|access-date=2023-02-12|website=SFGATE|language=en-US}}</ref> [[Hokky Situngkir]] also suggested the similar properties in Indonesian traditional art, [[batik]], and [[ornament (art)|ornaments]] found in traditional houses.<ref>Situngkir, Hokky; Dahlan, Rolan (2009). ''Fisika batik: implementasi kreatif melalui sifat fraktal pada batik secara komputasional''. Jakarta: Gramedia Pustaka Utama. {{ISBN|978-979-22-4484-7}}</ref><ref>{{cite news |last=Rulistia |first=Novia D. |date=October 6, 2015 |title=Application maps out nation's batik story |url=http://www.thejakartapost.com/news/2015/10/06/application-maps-out-nation-s-batik-story.html |newspaper=The Jakarta Post |access-date=September 25, 2016}}</ref>

Ethnomathematician Ron Eglash has discussed the planned layout of [[Benin city]] using fractals as the basis, not only in the city itself and the villages but even in the rooms of houses. He commented that "When Europeans first came to Africa, they considered the architecture very disorganised and thus primitive. It never occurred to them that the Africans might have been using a form of mathematics that they hadn't even discovered yet."<ref>Koutonin, Mawuna (March 18, 2016). "Story of cities #5: Benin City, the mighty medieval capital now lost without trace". Retrieved April 2, 2018.</ref>

In a 1996 interview with [[Michael Silverblatt]], [[David Foster Wallace]] explained that the structure of the first draft of ''[[Infinite Jest]]'' he gave to his editor Michael Pietsch was inspired by fractals, specifically the [[Sierpinski triangle]] (a.k.a. Sierpinski gasket), but that the edited novel is "more like a lopsided Sierpinsky Gasket".<ref name="novel">{{cite web |url=http://www.kcrw.com/etc/programs/bw/bw960411david_foster_wallace |first=David Foster |last=Wallace |title=Bookworm on KCRW |date=August 4, 2006 |publisher=Kcrw.com |access-date=October 17, 2010 |archive-date=November 11, 2010 |archive-url=https://web.archive.org/web/20101111033857/http://www.kcrw.com/etc/programs/bw/bw960411david_foster_wallace |url-status=dead }}</ref>

Some works by the Dutch artist [[M. C. Escher]], such as [[Circle Limit III]], contain shapes repeated to infinity that become smaller and smaller as they get near to the edges, in a pattern that would always look the same if zoomed in.

Aesthetics and Psychological Effects of Fractal Based Design:<ref>{{Cite journal |last1=Robles |first1=Kelly E. |last2=Roberts |first2=Michelle |last3=Viengkham |first3=Catherine |last4=Smith |first4=Julian H. |last5=Rowland |first5=Conor |last6=Moslehi |first6=Saba |last7=Stadlober |first7=Sabrina |last8=Lesjak |first8=Anastasija |last9=Lesjak |first9=Martin |last10=Taylor |first10=Richard P. |last11=Spehar |first11=Branka |last12=Sereno |first12=Margaret E. |date=2021 |title=Aesthetics and Psychological Effects of Fractal Based Design |journal=Frontiers in Psychology |volume=12 |doi=10.3389/fpsyg.2021.699962 |pmid=34484047 |pmc=8416160 |issn=1664-1078 |doi-access=free }}</ref> Highly prevalent in nature, fractal patterns possess self-similar components that repeat at varying size scales. The perceptual experience of human-made environments can be impacted with inclusion of these natural patterns. Previous work has demonstrated consistent trends in preference for and complexity estimates of fractal patterns. However, limited information has been gathered on the impact of other visual judgments. Here we examine the aesthetic and perceptual experience of fractal ‘global-forest’ designs already installed in humanmade spaces and demonstrate how fractal pattern components are associated with positive psychological experiences that can be utilized to promote occupant well-being. These designs are composite fractal patterns consisting of individual fractal ‘tree-seeds’ which combine to create a ‘global fractal forest.’ The local ‘tree-seed’ patterns, global configuration of tree-seed locations, and overall resulting ‘global-forest’ patterns have fractal qualities. These designs span multiple mediums yet are all intended to lower occupant stress without detracting from the function and overall design of the space. In this series of studies, we first establish divergent relationships between various visual attributes, with pattern complexity, preference, and engagement ratings increasing with fractal complexity compared to ratings of refreshment and relaxation which stay the same or decrease with complexity. Subsequently, we determine that the local constituent fractal (‘tree-seed’) patterns contribute to the perception of the overall fractal design, and address how to balance aesthetic and psychological effects (such as individual experiences of perceived engagement and relaxation) in fractal design installations. This set of studies demonstrates that fractal preference is driven by a balance between increased arousal (desire for engagement and complexity) and decreased tension (desire for relaxation or refreshment). Installations of these composite mid-high complexity ‘global-forest’ patterns consisting of ‘tree-seed’ components balance these contrasting needs, and can serve as a practical implementation of biophilic patterns in human-made environments to promote occupant well-being.

{{anchor|fractals in technology}}

<gallery heights="140" mode="packed">
File:Animated fractal mountain.gif|A fractal that models the surface of a mountain (animation)
File:FRACTAL-3d-FLOWER.jpg|3D recursive image
File:Fractal-BUTTERFLY.jpg|Recursive fractal butterfly image
File:Apophysis-100303-104.jpg|A [[fractal flame]]
</gallery>