## Jeffrey Stewart Ely |

Photographic Paper, 20” X 20” , 2009.

Julia sets are usually depicted two-dimensionally, either flat
or as textures on other surfaces which themselves may have little
to do with the Julia set. Here, we iterate the complex variable
relation,
new s = s^{2} - 1.25
thirteen times to produce a polynomial in the original variable, s,
of degree 8192.

Now consider the three-dimensional surface,
z = f(x,y) = |s^{8192} + ... |
where s = x+iy and | | denotes absolute value.
This picture is the graph of
(x,y, z) if z ≤ t
and
(x,y, t(t/z)^{p}) if z > t

where t is a threshold value ~1.464 and p = (1/2)^{13}

Jeffrey Stewart Ely, Associate Professor of Computer Science

Mathematical Sciences Department, Lewis and Clark College

Portland, Oregon

"I am interested in applying computer graphical techniques to
illuminate mathematical processes. Ideally, this can lead to
a deeper understanding of the process, but even if no new
insight is forthcoming, I am frequently mesmerized by the
compelling beauty of the unusual shapes.

I do not use 'canned' software. I wrote the code to first
principles in the 'C' programming language. This particular
image was constructed as a particle system made from 266
billion points and took 67 hours to compute."