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

I am a Designer, Engineer … CCD Camera, Bell Labs, 1973 Soda Hall, Berkeley, 1994 RISC chip, Berkeley, 1981 “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, “Hyperbolic Hexagon II ”B. Collins

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 Example: “Vox Solis” Layered laminated main shape Wood master pattern for sculpture

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

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. Profiled Slice through “Heptoroid”

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=1 B=2 B=3 B=4

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

“Cohesion” SIGGRAPH’2003 Art Gallery

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

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

Symmetries on the Sphere ISIS Symmetry Congress, Sydney, 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

3D Visualization Models of the Regular Polytopes in  4 D BRIDGES_5, Towson MD, 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 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 !”