Editing Pattern (section)

== Science and mathematics ==
[[File:Fractal fern explained.png|thumb|upright|Fractal model of a fern illustrating [[self-similar]]ity]]

[[Mathematics]] is sometimes called the "Science of Pattern", in the sense of rules that can be applied wherever needed.<ref>{{cite journal | title=Mathematics as a Science of Patterns: Ontology and Reference | author=Resnik, Michael D. | journal=Noûs |date=November 1981 | volume=15 | issue=4 | pages=529–550 | doi=10.2307/2214851| jstor=2214851 }}</ref> For example, any [[sequence]] of numbers that may be modeled by a mathematical function can be considered a pattern. Mathematics can be taught as a collection of patterns.<ref>{{cite web | url=http://www.coas.howard.edu/mathematics/faculty/bayne/patterns.html | title=MATH 012 Patterns in Mathematics - spring 2012 | year=2012 | access-date=16 January 2013 | author=Bayne, Richard E | archive-date=7 February 2013 | archive-url=https://web.archive.org/web/20130207065047/http://www.coas.howard.edu/mathematics/faculty/bayne/patterns.html | url-status=dead }}</ref>

[[Gravity]] is a source of ubiquitous scientific patterns or patterns of observation. The rising and falling pattern of the sun each day results from the rotation of the earth while in orbit around the sun. Likewise, the [[moon|moon's]] path through the sky is due to its orbit of the earth. These examples, while perhaps trivial, are examples of the "unreasonable effectiveness of mathematics" which obtain due to the [[differential equations]] whose application within [[physics]] function to describe the most general [[empirical]] patterns of the [[universe]].<ref>{{cite journal |last1 =Steen |first1 =Lynn |date =June 1988 |title =The Science of Patterns |url =https://www.science.org/doi/pdf/10.1126/science.240.4852.611 |journal =Science |volume =240 |issue =4852 |pages =611–616 |doi =10.1126/science.240.4852.611 |pmid =17840903 |bibcode =1988Sci...240..611S |access-date =2024-08-11|url-access =subscription }} The author attributes Eugene Wigner for the claim for the "unreasonable effectiveness of mathematics," a partial quote which continues "[t]he miracle of the appropriateness of the language of
mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve."</ref>

=== Real patterns<!--'Real patterns' redirects here--> ===
[[Daniel Dennett]]'s notion of '''real patterns'''<!--boldface per WP:R#PLA-->, discussed in his 1991 paper of the same name,<ref>Dennett, D. C. (1991). Real Patterns. ''The Journal of Philosophy'' '''88'''(1), 27–51.</ref> provides an ontological framework aiming to discern the reality of patterns beyond mere human interpretation, by examining their predictive utility and the efficiency they provide in compressing information. For example, [[Center of mass|centre of gravity]] is a real pattern because it allows the prediction of the movements of a bodies such as the earth around the sun, and it compresses all the information about all the particles in the sun and the earth that allows scientists to make those predictions.

=== Fractals ===

Some mathematical rule-patterns can be visualised, and among these are those that explain [[patterns in nature]] including the mathematics of symmetry, waves, meanders, and fractals. [[Fractal]]s are mathematical patterns that are scale-invariant. This means that the shape of the pattern does not depend on how closely you look at it. [[Self-similarity]] is found in fractals. Examples of natural fractals are coastlines and tree-shapes, which repeat their shape regardless of the magnification used by the viewer. While self-similar patterns can appear indefinitely complex, the rules needed to describe or produce their [[pattern formation|formation]] can be simple (e.g. [[Lindenmayer system]]s describing [[tree]]-shapes).<ref name="Mandelbrot1983">{{cite book |last =Mandelbrot |first =Benoit B. |author-link =Benoit Mandelbrot |title =The fractal geometry of nature
|url =https://books.google.com/books?id=0R2LkE3N7-oC |year =1983| publisher =Macmillan
|isbn =978-0-7167-1186-5}}</ref>

In [[pattern theory]], devised by [[Ulf Grenander]], mathematicians attempt to describe the world in terms of patterns. The goal is to lay out the world in a more computationally-friendly manner.<ref>{{cite book | title =Pattern Theory: From Representation to Inference | publisher =Oxford University Press |author1 =Grenander, Ulf |author2 =Miller, Michael | year =2007}}</ref>

In the broadest sense, any regularity that can be explained by a scientific theory is a pattern. As in mathematics, science can be taught as a set of patterns.<ref>{{cite web | url =http://www.cfa.harvard.edu/smg/Website/UCP/ | title =Causal Patterns in Science | publisher =Harvard Graduate School of Education | year =2008 | access-date =16 January 2013}}</ref>

A 2021 study, "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> suggested that 

<blockquote>
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 wellbeing. 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 wellbeing.
</blockquote>