# Hartmut F. W. Höft

Professor of Computer Science, retired

Eastern Michigan University

Ann Arbor, Michigan

I like to experiment with simple planar geometric figures. Starting with one outline I move it, rotate it, and change its proportions. With my images I want to demonstrate that applying elementary planar transformations to one simple shape produces complexity that can mask how the images were generated.

One special planar form is the ellipse: it is convex, has mirror symmetries and a shape that is easily manipulated through its two semi-axes. I move the centers of the ellipses along a closed, planar curve that I think of as the spine of the figures. Since the spine is not drawn, this one fundamental aspect of the images remains hidden to be discovered by a viewer. All images are mathematically planar.

One special planar form is the ellipse: it is convex, has mirror symmetries and a shape that is easily manipulated through its two semi-axes. I move the centers of the ellipses along a closed, planar curve that I think of as the spine of the figures. Since the spine is not drawn, this one fundamental aspect of the images remains hidden to be discovered by a viewer. All images are mathematically planar.

Evolution of the Twin Tornados

7.5 x 9 (10.5 x 12 framed) inches

archival photographic digital paper

2013

In this picture 12 images are arranged in a spiral. A primordial sea in the center starts the process. One parameter of the spine function increases, then stays constant, while the other increases and then decreases again. As the sequence progresses along the spiral the spine function increases in complexity so that the images billow out like clouds and then start separating into two funnels as the second parameter decreases again. Each image on the spiral is composed of 289 ellipses with a closed spine curve though it does not appear to be closed since the axes of the elipses decrease to zero at the bottom. The graphics were rendered in Mathematica 8 and printed on archival, photographic digital paper.

Elliptical Staircase (Study 11)

10 x 7.5 (13 x 10) inches

archival photographic digital paper

2013

In this image 720 ellipses are drawn in the plane along a closed spine with 11 lobes. At the middle level of the image there is a single large ellipse although a viewer may see the illusion of a spiraling opening downward on the left and a like spiraling opening up. The closed spine is traversed three times. The graphics were rendered in Mathematica 8 and printed on archival, photographic digital paper.