< Fractals < Mathematics < group

Kleinian group[1]

algorithms

  • escape time by Jos Leys[2], FF discussion
  • "drawn up by a multiplication of two by two matrices representing Moebius transformation" [3]

Programs

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."[12]
  • Schottky group [13][14]

Video

images

References

  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. ↑ Kleinian and Quasi-Fuchsian Limit Sets: An Open Source Toolbox Genotype: 1.1.45 by Chris King
  12. ↑ mathoverflow question: why-are-fuchsian-groups-interesting
  13. ↑ The Fractal Nature of Schottky Groups John Conley May 31, 2013
  14. ↑ A New Algorithm for Rendering Kissing Schottky Groups by Kento Nakamura, and Kazushi Ahara
  15. ↑ Jos Leys kleinian galleries
This article is issued from Wikibooks. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.