Background
This image was created for
a
poster
announcing the
conference
Geometry
and Dynamics in Surfaces and 3-Manifolds (held at Brown
University, May 3-6, 2007).
The ray-traced image shows approximately 18000 overlapping coplanar
solid glass spheres in front of a page from William Thurston's 1980
Princeton lecture notes The Geometry and
Topology of Three-Manifolds (now available in
an electronic
version). The intersection of the spheres with the plane
containing their centers is a domain of discontinuity of a
quasi-Fuchsian group of genus 2 created by a shear-bend deformation of a Fuchsian group. (For related images and animations see Jeff Brock's Cinéma Kleinéen.)
Method
The following procedure was used to create the image:
- Compute generators of the quasi-Fuchsian group from the shear-bend parameters using Mathematica
- Generate the limit set as a postscript file, using Curt McMullen's program lim
- Convert the limit set to a list of (center,radius) tuples for the spheres, using lim2pov
- Scan the background from a mimeographed copy of Thurston's lecture notes (page 8.36 in the original numbering)
- Integrate the background image and spheres (with glass texture, refraction, reflection, etc.) in a POV-Ray scene file.
- Render horizontal slices of the scene in parallel on several computers (using a total of 726 CPU-hours)
- Combine the slices using assembleppm, and convert to a reasonable image format (PNG)
The source files, sphere data, and background image are available as a
compressed tarball:
bug-on-notes.tar.gz
