Through the use of internal stops, each arm is constrained to rotate a maximum of 68.75° (1/2 the Golden Angle) relative to its neighboring layer.
The Helicone is featured in an article in the New York Times.
Materials: laser-cut plywood, brass, beechwood
The Lollipopter is a multicolored, plastic version of the Helicone.
The Lollipopter is available at a number of retail venues, including online at Amazon.com.
Materials: polypropylene, stainless steel, ABS
HyperCycles is based on the Spirograph toy. HyperCycles is essentially a Spirograph inside a Spirograph. This configuration results in an additional periodicity, which allows for the creation of more complex curves, and less regular drawings.
HyperCycles is available for purchase at the National Museum of Mathematics' online store.
The transformations in this tower result from Incremental Drift, wherein each layer rotates slightly faster than the layer beneath it. There are 32 layers in this tower, so the top layer must make 32 complete revolutions before the tower returns to the same state.
Internal mechanism designed and fabricated by Paul Stepahin.
Material: laser-cut plywood
Transforming Sculpture (proposal)
Click on image to view the proposal