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
Limit set of a quasifuchsian group on the sphere
Schottky (Kleinian) group limit set in the plane
_group_limit_set_in_plane.png)
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
