Jeffrey Ely
I am interested in applying computer graphical techniques to
illuminate mathematical processes and objects. Ideally, this
can lead to a deeper understanding or at least to an increased
appreciation and awareness of the process or object.
Some of my projects are implemented as billions of particles,
others use the ray tracing technique and hundreds of millions
of rays. In either case, I do not use "canned" software,
preferring to write the code myself to first principles.
Most mathematical formulas generate shapes that can feel very
mechanical. In an
attempt to discover shapes that are more organic, we turned to a
natural shaping process,
the wind.
Just as sand dunes are created when the velocity vector field of
the wind acts on the
grains of sand on the beach, this image is the result of the
three-dimensional velocity
vector field,
dx/dt = -z*(1-y*y)
dy/dt = -x*(1-z*z)
dz/dt = y*(1-x*x)
acting for a time on the points of the unit sphere. The striations
on the shape are
more than just artistic license as they were originally
longitudinal lines on the sphere.