Mikael Vejdemo-Johansson
The advent of accessible automated tools — 3d printers, laser cutters, CNC-controlled mills, vinyl cutters, et.c. — that through the Maker movement reaches commodity prices opens up a number of new approaches to art: especially algorithmic and mathematical art works. The computational control allows us to write algorithms to generate concrete physical art; and their precision allows a higher resolution than what the eye can discern.
In my mathematical art I seek to reify the abstract, to make mathematical concepts and shapes available to touch, to trace, to twist and turn. To create physical artifacts meant for interaction to bring the complex closer and make the abstract concrete.
Morin and Apéry (1987) gave a family of parametrized surfaces that interpolate between Steiner's Roman Surface and Boy's Surface. All the surfaces in the parametrization are immersions of the real projective plane into 3-dimensional Euclidean space, but the Roman surface has a high degree singularity at the center which Boy's surface avoids.
Here, we reify the family by giving the two extremes as well as the 25%, 50% and 75% intermediate steps between the surfaces. By representing them as wire frames, the parametrization itself can be traced out and studied tangibly.