Fractals/Mathematics/group/Kleinian group

Kleinian group

algorithms

 * escape time by Jos Leys, FF discussion
 * "drawn up by a multiplication of two by two matrices representing Moebius transformation"
 * inverse algorithm
 * 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

 * Spirofractal
 * 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
 * Kleinian Groups Programs: Indra Version by D Wright
 * lim by Curtis McMullen
 * Kleinian and Quasi-Fuchsian Limit Sets: An Open Source Toolbox Genotype: 1.1.45 by Chris King
 * Arnaud Cheritat
 * Universal cover of Klein's quartic. and the code
 * shadertoy :
 * kleinian
 * soma-arc
 * soma-arc : SchottkyLink
 * A New Algorithm for Rendering Kissing Schottky Groups by Kento Nakamura, and Kazushi Ahara
 * KleinianWalkerWeb
 * webgl
 * Universal cover of Klein's quartic. CC-BY-SA Arnaud Chéritat
 * aplets by A.N.Anderson
 * CindyJS
 * Circles by Alessandro Rosa
 * maple
 * Yousi Daniel Hue
 * JS
 * Draw the limit set of a group of Möbius transformations by Tim Hutton

relation between kleinian group and fractals

 * "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."
 * Schottky group

Video

 * 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
 * An overview on complex Kleinian groups (Angel Cano)
 * Schottky Link - Introduction by soma
 * KleinianWalker - Introduction by soma

images

 * by Jos Lays
 * 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
 * SL(View) 0.4 by David Dumas

=References= Geometry, Topology and Dynamics of Character Varieties https://doi.org/10.1142/8445 | August 2012
 * Klein's Web Pages
 * Indra's Pearls Web Site
 * Non-Euclidean geometry and Indra's pearls By Caroline Series and David Wright
 * FF
 * 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
 * fractalforums.org : help-with-indras-pearls-by-david-mumford-caroline-series-and-david-wright