Editing Fractal dimension (section)

== History ==
The terms ''fractal dimension'' and ''fractal'' were coined by Mandelbrot in 1975,<ref name="Mandelbrot quote"/> about a decade after he published his paper on self-similarity in the coastline of Britain. Various historical authorities credit him with also synthesizing centuries of complicated theoretical mathematics and engineering work and applying them in a new way to study complex geometries that defied description in usual linear terms.<ref name="classics"/><ref name="Gordon"/><ref name="MacTutor"/> The earliest roots of what Mandelbrot synthesized as the fractal dimension have been traced clearly back to writings about nondifferentiable, infinitely self-similar functions, which are important in the mathematical definition of fractals, around the time that [[calculus]] was discovered in the mid-1600s.<ref name="Mandelbrot1983" />{{rp|405}} There was a lull in the published work on such functions for a time after that, then a renewal starting in the late 1800s with the publishing of mathematical functions and sets that are today called canonical fractals (such as the eponymous works of [[Helge von Koch|von Koch]],<ref name="von Koch paper"/> [[Sierpiński]], and [[Gaston Julia|Julia]]), but at the time of their formulation were often considered antithetical mathematical "monsters".<ref name="classics">
{{cite book
| editor-last = Edgar
| editor-first = Gerald
| title = Classics on Fractals
| publisher = Westview Press
| year = 2004| isbn = 978-0-8133-4153-8 }}
</ref><ref name="MacTutor">{{cite web
 |title=A History of Fractal Geometry 
 |work=MacTutor History of Mathematics 
 |author=Trochet, Holly 
 |archive-url=https://web.archive.org/web/20120312153006/http://www-groups.dcs.st-and.ac.uk/%7Ehistory/HistTopics/fractals.html
 |archive-date=12 March 2012
 |url=http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/fractals.html 
 |year=2009 
 |url-status=dead
}}
</ref> These works were accompanied by perhaps the most pivotal point in the development of the concept of a fractal dimension through the work of [[Felix Hausdorff|Hausdorff]] in the early 1900s who defined a "fractional" [[Hausdorff dimension|dimension]] that has come to be named after him and is frequently invoked in defining modern [[fractals]].<ref name="coastline"/><ref name="Mandelbrot1983"/>{{rp|44}}<ref name="Mandelbrot Chaos">
{{cite book
| last = Mandelbrot
| first = Benoit
| title = Fractals and Chaos
| publisher = Springer
| year = 2004
| isbn = 978-0-387-20158-0
| quote = A fractal set is one for which the fractal (Hausdorff-Besicovitch) dimension strictly exceeds the topological dimension
| page= 38}}</ref><ref name = "Gordon">{{cite book
| last = Gordon
| first = Nigel
| title = Introducing fractal geometry
| publisher = Icon
| location = Duxford
| year = 2000
| isbn = 978-1-84046-123-7
| page = [https://archive.org/details/introducingfract0000lesm/page/71 71]
| url = https://archive.org/details/introducingfract0000lesm/page/71
}}</ref>

''See [[fractal#history|Fractal history]] for more information''

{{anchor|calculations}}