John Sullivan

Mathematical Visualization in Snow

2004: Turning a Snowball Inside Out

31 Jan 2004: We worked from 6-10am straightening struts and finishing the surface. Judging was 10-12, and the awards ceremony at 3pm. First place went to a team from British Columbia, second place to the Tennessee team, and third to the Ontario team. We received a special award for "Most Ambitious Piece", which came with a bottle of champagne! The picture to the right was taken after the evening banquet, when a dusting of powdery snow had already fallen on top of our nicely smoothed lines.

Selected daily photos. Sullivan's complete daily photos.

30 Jan 2004: We finished carving out the interior of the first hollow lobe (on the shady NE side), put a nice finish on those sturts, and started carving out the windows on the opposite SW lobe.

Selected daily photos. Sullivan's complete daily photos.

29 Jan 2004: After finishing carving out the ears, we used cloth strips to mark struts on the two lobes that were to be hollowed out; then we carved windows on one lobe. Another long day of hard work.

Selected daily photos. Sullivan's complete daily photos.

28 Jan 2004: We rounded off all the corners, basically leaving the convex hull of each of the four lobes of the Morin surface. We also dug most of the tunnels at ground level between the lobes, and started punching out the centers of the ears. A long 12-hour day of hard work.

Selected daily photos. Sullivan's complete daily photos.

27 Jan 2004: We cut four large wedges out of the cube of snow. The difficulty was that each of the eight bounding planes was titled.

Selected daily photos. Sullivan's complete daily photos.

25-26 Jan 2004: Team Minnesota arrived in Colorado, and carved a half-size practice block. We learned a lot about the strategies we might choose for the full-size sculpture.

Selected daily photos.

At the end of January 2004, I participated for the first time in the International Snow Sculpture Championships in Breckenridge, Colorado, USA. (See also another local webpage.) I was part of "Team Minnesota", led by Stan Wagon, a mathematician at Macalester College in Minnesota, who has entered the competition for 6 years in a row now, doing a mathematical visualization in snow sculpture each year. Stan has nice online reports about the team's past work, including a silver-medal winner in 2003. In 2004, we were one of 13 teams chosen by the organizers to enter this competition.

Our entry this year, entitled Turning a Snowball Inside Out is a depiction of a Morin surface. This is a halfway model for a sphere eversion, as originally envisioned by Bernard Morin. It is an immersed sphere with four lobes; two show the outside surface of the sphere and the other two show the inside surface. We used a similar Morin surface (but with minimum possible bending energy) in our 1998 video The Optiverse. A sphere eversion is a mathematical process of turning a spherical surface inside out. Physically, a closed surface like a sphere would have to be cut open to be turned inside out. But for our mathematical surface, cutting, tearing and creasing are not allowed; instead, parts of the surface are allowed to pass through other parts without even noticing. I wrote a more complete description of sphere eversions for The Optiverse.

We started with a 20-ton, 3x3x4 meter block of compressed snow. In the space of a few days, working against the clock and against the danger of too much sunlight, we carved the Morin surface. In our snowy representation, one side of the spherical surface was a solid surface, while the other side was represented by a rectangular grid of beams.

A Morin surface is merely a topological notion; in The Optiverse we used the Morin surface of least bending energy. Since the snow sculpture, unlike the sphere in the video, is static, showing just the halfway stage and not the whole eversion process, for Breckenridge we have decided to sculpt a different, more open shape of Morin surface, designed by team representative Carlo Séquin, who has a nice description of the design online. The photograph above shows a computer-generated macquette of the final design.

Please check back here, and at Stan and Carlo's webpages, for daily updates during the competition, 27 January through 1 February.