David Swart
I am a visual artist / photographer that creates mathematical artwork. I prefer to "grow my own" software which allows me the flexibility to explore or enhance new and existing mathematical ideas.
My goal is to create visual puzzles that demonstrate the fascinating aspects of themes that interest me -- including but not limited to reflections, spherical geometry, image transformations, and spherical panoramas.
When someone sees my work, I hope their first reaction is that they feel the piece looks nice, followed closely by, "hey, what's going on?" and ideally followed up with either a new understanding, or more questions about the mathematics and the ideas behind it.
2D TSP Art techniques are extended to the sphere. The "Yin-Yang circle packing method" presented by Michael Longuet-Higgins at Bridges 2010 was adapted to distribute the cities onto the sphere, and the final models were generated using custom software.
The patterns chosen are two-tone patterns: the familiar soccerball pattern, the pattern depicting the icosahedral symmetry groups, and appropriately enough for a travelling saleman, the world.
This is joint work with Pam Eveleigh. Her original photograph of a six pointed snowflake is transformed into eleven new versions with varying rotational symmetries. Conformal mappings are used here to avoid any stretching artifacts and consequently to avoid any evidence of "image tinkering". This exercise is done somewhat ironically and with some chagrin considering the plethora of improperly rendered non-six-pointed snowflakes in design and advertising. To anyone familiar with actual snow crystals, these new versions will seem "wrong". Alternatively one can consider these as attractive examples of what snowflakes would look like in a world where six pointed ice crystals were not the norm.
A stereographic projection of a spherical panorama centered on the zenith point: If we think of the visible sphere as a translucent sphere around the observer's head with imagery printed on it that matches the observer's surroundings: then this is what we would see on an imaginary ceiling if we were to shine a lamp from the sphere's lowest point.
This composition takes advantage of the conformal properties of the stereographic projection: we see that each detail in the panorama remains undistorted (particularly the two boys).