Fractals/Mathematics/group/Kleinian group
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Kleinian group^{[1]}
algorithms
[edit  edit source] escape time by Jos Leys^{[2]}, FF discussion
 "drawn up by a multiplication of two by two matrices representing Moebius transformation" ^{[3]}
 inverse algorithm ^{[4]}
 Drawing limit sets of Kleinian groups using finite state automata by Greg McShane, John R. Parker, Ian Redfern
 Kleinian circle packings by John R. Parker
 An indexbased revisitation by Alessandro Rosa
Programs
[edit  edit source] Spirofractal^{[5]}^{[6]}
 xenodream  Unique 3D graphics software gives you results that would be difficult or impossible using other tools, and more fun doing it.
 kleinian by Danny Calegari^{[7]}^{[8]}
 Kleinian Groups Programs: Indra Version by D Wright ^{[9]}^{[10]}
 lim by Curtis McMullen^{[11]}
 Kleinian and QuasiFuchsian Limit Sets: An Open Source Toolbox Genotype: 1.1.45 by Chris King^{[12]}
 Arnaud Cheritat
 shadertoy :
 somaarc
 webgl
 maple
 JS
relation between kleinian group and fractals
[edit  edit source] "for Fuchsian groups of the first kind, the limit set has Hausdorff dimension 1, i.e., it is not fractal.
 ... for all other quasifuchsian groups of the first kind, the limit set has Hausdorff dimension strictly bigger than 1, by a theorem of Rufus Bowen."^{[13]}
 Schottky group ^{[14]}^{[15]}
Video
[edit  edit source] vimeo album NonEuclidean Tessellations Tessellations of Kleinian Groups.
 Indra's Pearls fractal animation by FreymanArt
 Indra's Pearls: A Mathematical Adventure
 youtube search kleinian
 Schottky Link  Introduction by soma
 KleinianWalker  Introduction by soma
images
[edit  edit source] by Jos Lays^{[16]}
 by Curtis McMullen
 True 3d kleinians can be produced with surfbox by pupukuusikko
 Kleinian and QuasiFuchsian Limit Sets: An Open Source Toolbox Genotype: 1.1.32 by Chris King
 Generation of Limit Sets of Kleinian Groups Using a Feedback Loop Approach  java screipt
 David Dumas

Limit set of a quasifuchsian group on the sphere

Schottky (Kleinian) group limit set in the plane
References
[edit  edit source] ↑ Kleinian group in wikipedia
 ↑ A fast algorithm for limit sets of Kleinian groups with the Maskit parametrisation. Jos Leys January 2017
 ↑ hiddendimension : KleinianGroup_Fractals
 ↑ fractalforums.org : kleinianadventuresthreegeneratormaskit
 ↑ http://www.alunw.freeuk.com/fractalgallery.html
 ↑ openprocessing code
 ↑ GLUT Kleinian group visualizer by Danny Calegari
 ↑ kleinian, a tool for visualizing Kleinian groups Posted on March 4, 2014 by Danny Calegari
 ↑ kleinian by D Wright
 ↑ FRactal forum : Kleinian groups  an immense collection with sources!
 ↑ Programs by Curtis McMullen
 ↑ Kleinian and QuasiFuchsian Limit Sets: An Open Source Toolbox Genotype: 1.1.45 by Chris King
 ↑ mathoverflow question: whyarefuchsiangroupsinteresting
 ↑ The Fractal Nature of Schottky Groups John Conley May 31, 2013
 ↑ A New Algorithm for Rendering Kissing Schottky Groups by Kento Nakamura, and Kazushi Ahara
 ↑ Jos Leys kleinian galleries
 Klein's Web Pages
 The FareyFord tessellation and circle packing
 Chapter : Klienian goups in book Geometry and topology of threemanifolds By William Thurston
 The Group Properties Wiki
 wiki
 algorithms by A N Anderson
 Interaktive Materialien zum Buch Indra's Pearls by StefanLembach  12 May 2010
 COMPLEX KLEINIAN GROUPS by Angel Cano , JuanPablo Navarrete, Jos´e Seade
 FF : kleinianadventuresthreegeneratormaskit by xenodreambuie
 CREATING SOFTWARE FOR VISUALIZING KLEINIAN GROUPS by Yasushi Yamashita, in Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore: Volume 23
Geometry, Topology and Dynamics of Character Varieties https://doi.org/10.1142/8445  August 2012