# 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]}

## 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 Quasi-Fuchsian Limit Sets: An Open Source Toolbox Genotype: 1.1.45 by Chris King
^{[12]} - Arnaud Cheritat
- shadertoy :
- soma-arc
- 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 Non-Euclidean 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 Quasi-Fuchsian 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

# 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 : kleinian-adventures-three-generator-maskit
- ↑ 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 Quasi-Fuchsian Limit Sets: An Open Source Toolbox Genotype: 1.1.45 by Chris King
- ↑ mathoverflow question: why-are-fuchsian-groups-interesting
- ↑ 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 Farey-Ford tessellation and circle packing
- Chapter : Klienian goups in book Geometry and topology of three-manifolds 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 , Juan-Pablo Navarrete, Jos´e Seade
- FF : kleinian-adventures-three-generator-maskit 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