Examples of the algorithm for drawing image of Schottky groups by WebGL and GLSL.
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README.md

Iterated Inversion System

Examples of the algorithm for drawing image of Schottky groups by WebGL and GLSL. This is called Iterated Inversion System (IIS). It is easy to parallelize and render images fast. It can be used to render 2-dimensional kissing Schottky groups and also 3-dimensional kissing Schottky groups.
3D examples may require high GPU power, so run these examples at your own risk.
Similar examples are also available on my Shadertoy page. You can edit and run code easily. Some examples may run faster than running on my WebGL implementation.

Publication

  • Kento Nakamura and Kazushi Ahara, A New Algorithm for Rendering Kissing Schottky Groups, Bridges Finland 2016 Short Papers

Related project

  • Schottky Link
    An interactive visualization system on a family of Kleinian groups based on Schottky groups

Examples

Kissing Schottky

This is basic kissing Schottky group composed by four circles.

Orbit of the Schottky circles

Kissing Schottky

Limit set

Kissing Schottky limit set

Apollonian packing

This pattern is called apollonian packing. There are other algorithms for displaying it. Apollonian packing

Group composed by 9 circles

Actually, this is not Schottky group because Schottky groups are composed by even number of circles/spheres. However we can use this algorithm if groups are composed by circles/spheres.
Nine Circles

3D kissing Schottky based on octahedron

This group is composed by 6 Schottky spheres at the position of the vertexes of an octahedron.

Orbit of a sphere

3D kissing Schottky oct

Limit set

3D kissing Schottky oct limit set

Extra

Depending on the parameter, we can get such interesting image. 3D kissing Schottky oct ext

3D kissing Schottky based on cube

This group is composed by 8 Schottky spheres at the position of the vertexes of a cube.

Orbit of a sphere

3D kissing Schottky cube 2

Limit set

3D kissing Schottky cube 2

Indra's Bubbles

Tokyo Demo Fest 2016 GLSL Graphics Compo 2nd Place.
This demo is using this algorithm. Nine Circles

License

Indra's Bubbles

Creative Commons Attribution-ShareAlike 3.0 Unported

Others

MIT