Editing Mandelbrot set (section)

===Self-similarity===
[[File:Self-Similarity-Zoom.gif|right|thumb|[[Self-similarity]] in the Mandelbrot set shown by zooming in on a round feature while panning in the negative-''x'' direction. The display center pans left from the fifth to the seventh round feature (−1.4002,&nbsp;0) to (−1.4011,&nbsp;0) while the view magnifies by a factor of 21.78 to approximate the square of the [[Feigenbaum constants|Feigenbaum ratio]].]]
The Mandelbrot set is [[self-similar]] under magnification in the neighborhoods of the [[Misiurewicz point]]s. It is also conjectured to be self-similar around generalized [[Feigenbaum point]]s (e.g., −1.401155 or −0.1528&nbsp;+&nbsp;1.0397''i''), in the sense of converging to a limit set.<ref>{{cite journal | last1 = Lei | year = 1990 | title = Similarity between the Mandelbrot set and Julia Sets | url = http://projecteuclid.org/euclid.cmp/1104201823| journal = Communications in Mathematical Physics | volume = 134 | issue = 3| pages = 587–617 | doi=10.1007/bf02098448| bibcode = 1990CMaPh.134..587L| s2cid = 122439436 }}</ref><ref>{{cite book |author=J. Milnor |chapter=Self-Similarity and Hairiness in the Mandelbrot Set |editor=M. C. Tangora |location=New York |pages=211–257 |title=Computers in Geometry and Topology |url=https://books.google.com/books?id=wuVJAQAAIAAJ |year=1989|publisher=Taylor & Francis|isbn=9780824780319 }})</ref> The Mandelbrot set in general is quasi-self-similar, as small slightly different versions of itself can be found at arbitrarily small scales. These copies of the Mandelbrot set are all slightly different, mostly because of the thin threads connecting them to the main body of the set.<ref>{{Cite web |title=Mandelbrot Viewer |url=https://math.hws.edu/eck/js/mandelbrot/MB.html |access-date=2025-03-01 |website=math.hws.edu}}</ref>