Fractals/Mathematics/group/Kleinian group
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 index-based 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 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
-
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 | 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