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]

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]

images[edit | edit source]

References[edit | edit source]

  1. Kleinian group in wikipedia
  2. A fast algorithm for limit sets of Kleinian groups with the Maskit parametrisation. Jos Leys January 2017
  3. hiddendimension : KleinianGroup_Fractals
  4. fractalforums.org : kleinian-adventures-three-generator-maskit
  5. http://www.alunw.freeuk.com/fractalgallery.html
  6. openprocessing code
  7. GLUT Kleinian group visualizer by Danny Calegari
  8. kleinian, a tool for visualizing Kleinian groups Posted on March 4, 2014 by Danny Calegari
  9. kleinian by D Wright
  10. FRactal forum : Kleinian groups - an immense collection with sources!
  11. Programs by Curtis McMullen
  12. Kleinian and Quasi-Fuchsian Limit Sets: An Open Source Toolbox Genotype: 1.1.45 by Chris King
  13. mathoverflow question: why-are-fuchsian-groups-interesting
  14. The Fractal Nature of Schottky Groups John Conley May 31, 2013
  15. A New Algorithm for Rendering Kissing Schottky Groups by Kento Nakamura, and Kazushi Ahara
  16. Jos Leys kleinian galleries

Geometry, Topology and Dynamics of Character Varieties https://doi.org/10.1142/8445 | August 2012