朱利亚集合（又译为茹利亚集合，）是一个在复平面上形成分形的点的集合。以法国数学家的名字命名。
定义
對於任意複變函數f，其朱利亞集合為所有不導致數列f(f(f\ldots(z)))發散的z所構成的集合。
以下列函數為例：
:f_c(z)= z^2 + c
对于固定的复数c，取某一 z 值（如z=z_0），可以得到序列
:z_0, f_c(z_0), f_c(f_c(z_0)), f_c(f_c(f_c(z_0))), \ldots .
这一序列可能發散于无穷大或始终处于某一范围之内并收敛于某一值。将使其不扩散的z值的集合称为朱利亚集合。
示例
下面各图显示了c取不同值时所得到的不同的朱利亚集合在复平面上的图像：
Image:Julia (Fractal).png
Image:Julia set (C = 0.285, 0.01).jpg
Image:Julia set (C = 0.285, 0.01) II.jpg
Image:Julia set (Detail 01).jpg
Image:Julia set (Detail 02).jpg
Image:Julia set (highres 01).jpg
Image:Julia set (highres 02).jpg
Image:Julia set (Rev formula 01).jpg
Image:Julia set (Rev formula 02).jpg
Image:Julia set (Rev formula 03).jpg
Image:Julia set (Rev formula 04).gif
Image:Julia-Teppich.png
Image:Reversed Julia set C = ( 0.4 0.3 ).gif
Image:Fractals-julia-still.gif
Image:Fractals-julia.gif
Image:Julia set (indigo).png
Image:Julia set (ice).png
Image:Julia set (chartreuse).png
Image:Julia set (red).png
Image:Time escape Julia set from coordinate (phi-2, phi-1).jpg
Image:Julia-Menge.png
Image:Time escape Julia set from coordinate (0.285, 0).jpg
Image:Mandelbrot and Julia.png
Image:Julia set (No detail 01).jpg
Image:Julia set (No detail 02).jpg
参考
外部連結
*
*
[http://paulbourke.net/fractals/juliaset/ Julia Set Fractal (2D)*] , Paul Bourke
[http://mathmo.blogspot.com/2007/04/essay-backtrack-julia-sets.html Julia Sets*] , Jamie Sawyer
[http://mcgoodwin.net/julia/juliajewels.html Julia Jewels: An Exploration of Julia Sets*] , Michael McGoodwin
*[http://www.lucypringle.co.uk/photos/1996/uk1996ck.shtml Crop circle Julia Set] , Lucy Pringle
*[https://web.archive.org/web/20120326020259/http://www.hightechdreams.com/weaver.php?topic=fractals Interactive Julia Set Applet], Josh Greig
*[http://aleph0.clarku.edu/~djoyce/julia/explorer.html Julia and Mandelbrot Set Explorer] , David E. Joyce
*[https://web.archive.org/web/20110317020756/http://www.lizardie.com/links/download/fractal-generator A simple program to generate Julia sets (Windows, 370 kb)]
*[http://ifs-tools.sourceforge.net/ A collection of applets] one of which can render Julia sets via Iterated Function Systems.
*[https://web.archive.org/web/20110218135200/http://juliamap.googlelabs.com/ Julia meets HTML5 ] Google Labs' HTML5 Fractal generator on your browser
*[https://cran.r-project.org/web/packages/Julia/index.html Julia] GNU R Package to generate Julia or Mandelbrot set at a given region and resolution.
*[http://dvdpedia.de/julia/julia.html Julia sets] A visual explanation of Julia Sets.
*[https://7affer.github.io/fractalTS/ FractalTS] Mandelbrot, Burning ship and corresponding Julia set generator.
*[http://julia.finengin.net Julia set images online rendering]
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