Fractals/Mathematics/group/Kleinian group

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Kleinian group[1]

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]

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]

images[edit]

References[edit]

  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. http://www.alunw.freeuk.com/fractalgallery.html
  5. openprocessing code
  6. GLUT Kleinian group visualizer by Danny Calegari
  7. kleinian, a tool for visualizing Kleinian groups Posted on March 4, 2014 by Danny Calegari
  8. kleinian by D Wright
  9. FRactal forum : Kleinian groups - an immense collection with sources!
  10. Programs by Curtis McMullen
  11. mathoverflow question: why-are-fuchsian-groups-interesting
  12. The Fractal Nature of Schottky Groups John Conley May 31, 2013
  13. A New Algorithm for Rendering Kissing Schottky Groups by Kento Nakamura, and Kazushi Ahara
  14. Jos Leys kleinian galleries