查看“︁朱利亚集合”︁的源代码

{{NoteTA|G1=Math}}
[[File:Julia-Set z2+c ani.gif|thumb|right|250px|朱利亚集合的動態影像]]
'''朱利亚集合'''（又译为'''茹利亚集合'''，{{lang-en|Julia set}}）是一个在[[复平面]]上形成[[分形]]的点的集合。以[[法国]]数学家[[加斯顿·朱利亚]]（Gaston Julia）<ref>Gaston Julia (1918) "Mémoire sur l'iteration des fonctions rationnelles," ''Journal de Mathématiques Pures et Appliquées'', vol. 8, pages 47-245.</ref>的名字命名。

== 定义 ==
朱利亚集合可以由下式进行反复迭代得到：
:<math>f_c(z)= z^2 + c</math>

对于固定的[[复数 (数学)|复数]]<math>c</math>，取某一 <math>z</math> 值（如<math>z=z_0</math>），可以得到[[序列]]
:<math>z_0, f_c(z_0), f_c(f_c(z_0)), f_c(f_c(f_c(z_0))), \ldots .</math>

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。我们将使其不扩散的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：
{{commons|Julia set}}

<gallery>
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
</gallery>

== 参考 ==

{{reflist}}

==外部連結==
{{Wikibooks|Fractals}}
* {{springer|title=Julia set|id=p/j054390}}
*{{mathworld | urlname = JuliaSet | title = Julia Set}}
*[http://paulbourke.net/fractals/juliaset/ ''Julia Set Fractal (2D)''] {{Wayback|url=http://paulbourke.net/fractals/juliaset/ |date=20201118045716 }}, Paul Bourke
*[http://mathmo.blogspot.com/2007/04/essay-backtrack-julia-sets.html ''Julia Sets''] {{Wayback|url=http://mathmo.blogspot.com/2007/04/essay-backtrack-julia-sets.html |date=20210224084441 }}, Jamie Sawyer
*[http://mcgoodwin.net/julia/juliajewels.html ''Julia Jewels: An Exploration of Julia Sets''] {{Wayback|url=http://mcgoodwin.net/julia/juliajewels.html |date=20210224011916 }}, Michael McGoodwin
*[http://www.lucypringle.co.uk/photos/1996/uk1996ck.shtml Crop circle Julia Set] {{Wayback|url=http://www.lucypringle.co.uk/photos/1996/uk1996ck.shtml |date=20171115211734 }}, 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] {{Wayback|url=http://aleph0.clarku.edu/~djoyce/julia/explorer.html |date=20081020063607 }}, 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] {{Wayback|url=http://ifs-tools.sourceforge.net/ |date=20210224054551 }} 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] {{Wayback|url=https://cran.r-project.org/web/packages/Julia/index.html |date=20210227021958 }} GNU R Package to generate Julia or Mandelbrot set at a given region and resolution.
*[http://dvdpedia.de/julia/julia.html Julia sets] {{Wayback|url=http://dvdpedia.de/julia/julia.html |date=20170616200359 }} A visual explanation of Julia Sets.
*[https://7affer.github.io/fractalTS/ FractalTS] {{Wayback|url=https://7affer.github.io/fractalTS/ |date=20210307222854 }} Mandelbrot, Burning ship and corresponding Julia set generator.
*[http://julia.finengin.net Julia set images online rendering] {{Wayback|url=http://julia.finengin.net/ |date=20190622031041 }}

{{分形}}

[[Category:分形]]