"Julia"

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 = s² - 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) = |s⁸¹⁹² + ... | 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."