# Fractals/Mathematics/group/Kleinian group

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Kleinian group^{[1]}

## Contents

## algorithms[edit]

- escape time by Jos Leys
^{[2]}, FF discussion - "drawn up by a multiplication of two by two matrices representing Moebius transformation"
^{[3]}

## Programs[edit]

- Spirofractal
^{[4]}^{[5]} - kleinian
^{[6]}^{[7]} - Kleinian Groups Programs: Indra Version by D Wright
^{[8]}^{[9]} - lim by Curtis McMullen
^{[10]} - Arnaud Cheritat
- shadertoy :
- soma-arc

## relation between kleinian group and fractals[edit]

- "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."
^{[11]} - Schottky group
^{[12]}^{[13]}

## Video[edit]

- vimeo album Non-Euclidean Tessellations Tessellations of Kleinian Groups.
- Indra's Pearls fractal animation by FreymanArt
- youtube search kleinian

## images[edit]

- by Jos Lays
^{[14]} - 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

# References[edit]

- ↑ Kleinian group in wikipedia
- ↑ A fast algorithm for limit sets of Kleinian groups with the Maskit parametrisation. Jos Leys January 2017
- ↑ hiddendimension : KleinianGroup_Fractals
- ↑ 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
- ↑ 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