OZONE Meeting SIGGRAPH 2003 mathematics art Carlo H

OZONE Meeting, SIGGRAPH 2003 mathematics & art Carlo H. Séquin U. C. Berkeley

I am a Designer, Engineer … CCD Camera, Bell Labs, 1973 RISC chip, Berkeley, 1981 Soda Hall, Berkeley, 1994 “Octa-Gear”, Berkeley, 2000

“Artistic Geometry” The role of the computer in: u the creative process, u aesthetic optimization. Collaboration with…

Virtual Model Making for Mathematically Inspired Sculptures Art-Math'97, SUNY, Albany, 1997. B. Collins “Hyperbolic Hexagon II ”

Closing the Loop straight or twisted

Brent Collins’ Prototyping Process Armature for the "Hyperbolic Heptagon" Mockup for the "Saddle Trefoil" Time-consuming ! (1 -3 weeks)

“Sculpture Generator I”, GUI

V-art Virtual Glass Scherk Tower with Monkey Saddles (Radiance 40 hours) Jane Yen

Art, Math, and Computers BRIDGES’ 98, Winfield KS, July 29, 1998

Virtual Prototyping of Geom. Sculptures Computers & Sculpture, Chicago, 1998. Solar Arch (with Brent Collins)

Collins’ Fabrication Process Layered laminated main shape Wood master pattern for sculpture Example: “Vox Solis”

Slices through “Minimal Trefoil” 50% 30% 23% 10% 45% 27% 20% 5% 35% 25% 15% 2%

Profiled Slice through “Heptoroid” u One thick slice thru sculpture, from which Brent can cut boards and assemble a rough shape. u Traces represent: top and bottom, as well as cuts at 1/4, 1/2, 3/4 of one board.

Emergence of the “Heptoroid” (1) Assembly of the precut boards

Emergence of the “Heptoroid” (2) Forming a continuous smooth edge

Emergence of the “Heptoroid” (3) Smoothing the whole surface

The Finished “Heptoroid” u at Fermi Lab Art Gallery (1998).

Various “Scherk-Collins” Sculptures

Hyper-Sculpture: “Family of 12 Trefoils” W=2 W=1 B=2 B=3 B=4

Computer-Augmented Inspiration ISAMA 99, San Sebastian, 1999. Doubly-wound Scherk-Collins Toroid

“Cohesion” SIGGRAPH’ 2003 Art Gallery

Analogies from 2 D to 3 D: Exercises in Disciplined Creativity BRIDGES, Winfield KS, 1999. 3 D Yin-Yang

Turning Math Models into Sculptures MOSAIC 2000, Seattle, 2000. Triply Twisted Figure-8 Klein Bottle

Symmetries on the Sphere ISIS Symmetry Congress, Sydney, 2001. 60 Butterflies

Viae Globi - Pathways on a Sphere Mathematics and Design, Geelong, 2001.

Sculpture Design Virtual Systems & Multimedia, Berkeley, 2001 Galapagos (version 5), inspired by Brent Collins

3 D Visualization Models of the Regular Polytopes in 4 D BRIDGES_5, Towson MD, 2002. 4 D “ 120 -Cell”

Volution’s Evolution Meeting Alhambra, Granada, 2003

Modular Minimal Surfaces of Increasing Genus, Embedded in a Cube Volution_0 Volution_5

Whirled White Web: Art & Math in Snow-sculpting, Breckenridge, CO, 2003

The Winners 1 st: Canada – B. C. , 2 nd: USA – Minnesota, 3 rd: USA – Breckenridge “… sacred geometry … very intricate … very 21 st century !”