A New Algorithm for Rendering Kissing Schottky Groups

Aus de_evolutionary_art_org
Wechseln zu: Navigation, Suche


Kento Nakamura and Kazushi Ahara: A New Algorithm for Rendering Kissing Schottky Groups. In: Bridges 2016, Pages 367–370.



In this paper, we present an algorithm for drawing images of Schottky groups. This algorithm is called an Iterated Inversion System (IIS). It is easy to parallelize and renders images fast. It can be used to render 2-dimensional kissing Schottky groups and also 3-dimensional kissing Schottky groups.

Extended Abstract


 author      = {Kento Nakamura and Kazushi Ahara},
 title       = {A New Algorithm for Rendering Kissing Schottky Groups},
 pages       = {367--370},
 booktitle   = {Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture},
 year        = {2016},
 editor      = {Eve Torrence, Bruce Torrence, Carlo S\'equin, Douglas McKenna, Krist\'of Fenyvesi and Reza Sarhangi},
 isbn        = {978-1-938664-19-9},
 issn        = {1099-6702},
 publisher   = {Tessellations Publishing},
 address     = {Phoenix, Arizona},
 url         = {http://de.evo-art.org/index.php?title=A_New_Algorithm_for_Rendering_Kissing_Schottky_Groups },
 note        = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-367.html}}

Used References

[1] David Mumford, Caroline Series, David Wright, Indra’s Pearls (2002), Cambridge University Press.

[2] Kazushi Ahara, Yoshiaki Araki, Sphairahedral Approach to Parameterize Visible Three Dimensional Quasi-Fuchsian Fractals (2003), http://ieeexplore.ieee.org/xpl/freeabs_all.jsp? tp=&arnumber=1214471&isnumber=27295, IEEE Computer Graphics International

[3] Knighty, Another 3D Kleinian, http://www.fractalforums.com/ifs-iterated-function-systems/ another-3d-kleinian/ (as of Jan. 10 2016)

[4] Mikael H Christensen, Distance Estimated 3D Fractals (Part I), http://blog.hvidtfeldts.net/ index.php/2011/06/distance-estimated-3d-fractals-part-i/ (as of Jan. 10 2016)

[5] Kento Nakamura as soma arc, Indra’s Bubbles https://www.shadertoy.com/view/XsGGWG (as of March 4 2016)

[6] Kento Nakamura as soma-arc, Iterated Inversion System in GitHub, https://github.com/soma-arc/IteratedInversionSystem (as of March 4 2016)


Full Text


intern file

Sonstige Links