Editing Mandelbrot set (section)

==History==
[[File:Mandel.png|thumb|upright=1.35|The first published picture of the Mandelbrot set, by [[Robert W. Brooks]] and Peter Matelski in 1978]]
The Mandelbrot set has its origin in [[complex dynamics]], a field first investigated by the [[French mathematicians]] [[Pierre Fatou]] and [[Gaston Julia]] at the beginning of the 20th century. The fractal was first defined and drawn in 1978 by [[Robert W. Brooks]] and Peter Matelski as part of a study of [[Kleinian group]]s.<ref name=":0">Robert Brooks and Peter Matelski, ''The dynamics of 2-generator subgroups of PSL(2,C)'', in {{cite book|url=https://abel.math.harvard.edu/archive/118r_spring_05/docs/brooksmatelski.pdf|title=Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference|author=Irwin Kra|date=1981|publisher=Princeton University Press|others=[[Bernard Maskit]]|isbn=0-691-08267-7|editor=Irwin Kra|access-date=1 July 2019|archive-url=https://web.archive.org/web/20190728201429/http://www.math.harvard.edu/archive/118r_spring_05/docs/brooksmatelski.pdf|archive-date=28 July 2019|url-status=dead}}</ref> On 1 March 1980, at [[IBM]]'s [[Thomas J. Watson Research Center]] in [[Yorktown Heights, New York|Yorktown Heights]], [[New York (state)|New York]], [[Benoit Mandelbrot]] first visualized the set.<ref name="bf">{{cite journal |url=http://sprott.physics.wisc.edu/pubs/paper311.pdf |title=Biophilic Fractals and the Visual Journey of Organic Screen-savers |author=R.P. Taylor & J.C. Sprott |access-date=1 January 2009 |year=2008 |journal=Nonlinear Dynamics, Psychology, and Life Sciences |volume=12 |issue=1 |pages=117–129 |publisher=Society for Chaos Theory in Psychology & Life Sciences |pmid=18157930 }}</ref>

Mandelbrot studied the [[parameter space]] of [[quadratic polynomial]]s in an article that appeared in 1980.<ref>{{cite journal |first=Benoit |last=Mandelbrot |title=Fractal aspects of the iteration of <math>z\mapsto\lambda z(1-z)</math> for complex <math>\lambda, z</math> |journal=Annals of the New York Academy of Sciences |volume=357 |issue=1 |pages=249–259 |year=1980 |doi=10.1111/j.1749-6632.1980.tb29690.x |s2cid=85237669 }}</ref> The mathematical study of the Mandelbrot set really began with work by the mathematicians [[Adrien Douady]] and [[John H. Hubbard]] (1985),<ref name="John H. Hubbard 1985">Adrien Douady and John H. Hubbard, ''Etude dynamique des polynômes complexes'', Prépublications mathémathiques d'Orsay 2/4 (1984 / 1985)</ref> who established many of its fundamental properties and named the set in honor of Mandelbrot for his influential work in [[fractal geometry]].

The mathematicians [[Heinz-Otto Peitgen]] and [[Peter Richter]] became well known for promoting the set with photographs, books (1986),<ref>{{cite book |title=The Beauty of Fractals |last=Peitgen |first=Heinz-Otto |author2=Richter Peter |year=1986 |publisher=Springer-Verlag |location=Heidelberg |isbn=0-387-15851-0 |title-link=The Beauty of Fractals }}</ref> and an internationally touring exhibit of the German [[Goethe-Institut]] (1985).<ref>[[Frontiers of Chaos]], Exhibition of the Goethe-Institut by H.O. Peitgen, P. Richter, H. Jürgens, M. Prüfer, D.Saupe. Since 1985 shown in over 40 countries.</ref><ref>{{cite book |title=Chaos: Making a New Science |last=Gleick |first=James |year=1987 |publisher=Cardinal |location=London |pages=229 |title-link=Chaos: Making a New Science }}</ref>

The cover article of the August 1985 ''[[Scientific American]]'' introduced the [[algorithm]] for computing the Mandelbrot set. The cover was created by Peitgen, Richter and [[Dietmar Saupe|Saupe]] at the [[University of Bremen]].<ref>{{Cite journal|date=August 1985|title=Exploring The Mandelbrot Set|url=https://www.jstor.org/stable/24967754|journal=Scientific American|volume=253|issue=2|pages=4|jstor=24967754}}</ref> The Mandelbrot set became prominent in the mid-1980s as a [[Demo (computer programming)|computer-graphics demo]], when [[personal computer]]s became powerful enough to plot and display the set in high resolution.<ref>{{cite magazine |last=Pountain |first=Dick |date=September 1986 |title= Turbocharging Mandelbrot |url=https://archive.org/stream/byte-magazine-1986-09/1986_09_BYTE_11-09_The_68000_Family#page/n370/mode/1up |magazine= [[Byte (magazine)|Byte]] |access-date=11 November 2015 }}</ref>

The work of Douady and Hubbard occurred during an increase in interest in [[complex dynamics]] and [[abstract mathematics]],<ref name=rees>{{cite journal
 | last1 = Rees
 | first1 = Mary
    | author-link = Mary Rees
 | date = January 2016
    | title = One hundred years of complex dynamics
 | journal = [[Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences]]
 | volume =  472
 | issue = 2185
 | pages =
 | doi = 10.1098/rspa.2015.0453
 | pmid = 26997888
 | pmc = 4786033
 | bibcode = 2016RSPSA.47250453R
 }}</ref> and the topological and geometric study of the Mandelbrot set remains a key topic in the field of complex dynamics.<ref>{{Cite book |last=Schleicher |first=Dierk |url=https://books.google.com/books?id=Ek3rBgAAQBAJ |title=Complex Dynamics: Families and Friends |date=2009-11-03 |publisher=CRC Press |isbn=978-1-4398-6542-2 |pages=xii |language=en}}</ref>