# 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.