Some of Brent Collins' recent wood sculptures can be understood geometrically as rings of saddle surfaces resulting from a toroidal warping of a truncated Scherk minimal surface.
A computer program has been developed to visualize different configurations of such saddle rings with different number of holes and different amounts of twists. Experimenting with different values for the parameters of such a virtual sculpture can be done at interactive speeds and can save weeks of hard labor needed to build physical prototypes. It also may result in more optimized solutions, and it allows to find configurations that one would not likely dare to explore if the prototypes had to be built manually from physical matter.
An intellectual collaboration with Brent Collins has already resulted in a couple of intriguing new wood sculptures. A direct collaboration on more complex sculptures is now under way since the prototyping program has recently been enhanced to deliver construction blueprints in the form of slices through the sculpture geometry.
Here are two recent sculptures by Brent Collins photographed by Phillip Geller: followed by a simulation with our sculpture generator:
These sculptures can be understood as a toroidal warp of Scherk's 2nd minimal surface, possibly with an overall twist:
_ An early sculpture by Brent Collins had a similar structure, but used 3rd-order saddles (above).
And here is an entirely "virtual" sculpture with 5 stacked stories of monkey saddles, created by Séquin's generator:
Here again is the above 7-hole sculpture, but now with 450 degrees of twist:
An 8-storey Scherk tower warped into a toroid with 180 degrees of twist:
And a more complex structure using 5th order saddles presented in cross-eye stereo:
-->(see it in stereo)
Here is the result of a quest for some minimal structure with only 3 storeys:
And this is Collins' solution for the quest of finding a minimal structure, photographed from front and back by Phillip Geller:
Yet to be scanned in: a second solution by Brent Collins:
The next sculpture that I am working on with Brent Collins:
-->(see it in stereo)
And Collins' actual sculpture: