Stewart Dickson
110 N Whipple St
Fort Bragg, CA  95437
(707)813-0385
MathArtSPD@GMail.com

Portfolio of Variations on the Costa-Hoffman-Meeks Minimal Surfaces

Artist's Statement

Genus 4, Three-Ended Minimal Surface, Wavefront computer visualization, (c) 1990 David Hoffman, Stewart Dickson.

The database was created by David Hoffman and James T. Hoffman, University of Massachusetts and adapted for sculpture by Stewart Dickson.

Press Here for PostScript text on the mathmatics of minimal surfaces.

Software/Hardware used: Mathematical form discovered using Visual Programming Language (VPL) by James Hoffman on a Ridge 32/110 computer with Raster Technologies One/380 graphics controller. Computer rendering using the Wavefront Technologies Advanced Visualizer on a Silicon Graphics Iris 4D/70S compute server.

Genus 4, Three-Ended Minimal Surface, 5.4" X 8.5" X 8.5", Stereolithograph, (c) 1990 David Hoffman, Stewart Dickson. Press Here for price list.

A Stereolithograph is a direct, three-dimensional print created by a digital computer. It is a replica, accurate to within 0.01" of the three-dimensional computer data description of the object. The database was created by David Hoffman and James T. Hoffman, University of Massachusetts and adapted for sculpture by Stewart Dickson.

The material used in the Stereolithographic object building process, called SOMOS 2000, is an experimental polymer. Its properties over extended periods of time are unknown. Therefore, the artist considers the Stereolithograph essentially as a clay or wax first-generation impression, not a final presentation. Objects in Stereolithograph form are proposed to be cast into more durable metals.

Press Here for PostScript text on the mathmatics of minimal surfaces.

Software/Hardware used: Mathematical form discovered using Visual Programming Language (VPL) by James Hoffman on a Ridge 32/110 computer with Raster Technologies One/380 graphics controller. Database adapted for sculpture by Stewart Dickson using original C-language enhancements to the Wavefront modeling environment on a Silicon Graphics IRIS 3030. Stereolithography by DuPont SOMOS group, Wilmington, Delaware.

Genus 1, Four-Ended Minimal Surface Including a Topological Handle, Wavefront computer visualization, (c) 1990, David Hoffman, James Hoffman and Stewart Dickson.

The database was created by David Hoffman and James T. Hoffman, University of Massachusetts and adapted for sculpture by Stewart Dickson.

Software/Hardware used: Mathematical form discovered using Visual Programming Language (VPL) by James Hoffman on a Ridge 32/110 computer with Raster Technologies One/380 graphics controller. Computer rendering using the Wavefront Technologies Advanced Visualizer on a Silicon Graphics Iris 4D/70S compute server.

Genus 1, Four-Ended Minimal Surface Including a Topological Handle, Dimensions: (approx.) 18" X 18" X 18", Stereolithograph, (c) 1990 David Hoffman, James Hoffman and Stewart Dickson. Photo courtesy of Dr. Guy MacDonald, Johnson Controls, Inc. Press Here for price list.

A Stereolithograph is a direct, three-dimensional print created by a digital computer. It is a replica, accurate to within 0.01" of the three-dimensional computer data description of the object. The database was created bys David Hoffman and James T. Hoffman, University of Massachusetts and adapted for sculpture by Stewart Dickson.

Software/Hardware used: Mathematical form discovered using Visual Programming Language (VPL) by James Hoffman on a Ridge 32/110 computer with Raster Technologies One/380 graphics controller. Database adapted for sculpture by Stewart Dickson using original C-language enhancements to the Wavefront modeling environment on a Silicon Graphics IRIS 3030. Stereolithography by Johnson Controls, Inc., Milwaukee, Wisconsin.

Genus 1, Infinite-Ended Minimal Surface Including a Topological Handle, Wavefront computer visualization, (c) 1990 David Hoffman, Stewart Dickson.

This is actually sixteen instances of a single fundamental piece or symmetric decomposition, repeated through translations and rotations. The database was created by David Hoffman and James T. Hoffman, University of Massachusetts and adapted for sculpture by Stewart Dickson.

Hardware/Software used: Computer rendering using the Wavefront Technologies Advanced Visualizer on a Silicon Graphics Iris 4D/70S compute server.

Fundamental Piece, Genus 1, Infinite-Ended Minimal Surface Including a Topological Handle, 6.0" X 6.0" X 8.0", Stereolithograph, (c) 1991 David Hoffman, Stewart Dickson.

A Stereolithograph is a direct, three-dimensional print created by a digital computer. It is a replica, accurate to within 0.01" of the three-dimensional computer data description of the object. The database was created by David Hoffman and James T. Hoffman, University of Massachusetts and adapted for sculpture by Stewart Dickson.

The complete sculpture represented by this shape cannot be cast from a simple mould topology, neither has the Stereolithograph apparatus sufficient dimensional capacity to render the object satisfactorially large. The symmetric decomposition, however, can be reproduced in large numbers in wax from a simple, two-piece mould. The wax reproductions are assembled via symmetric translations and rotations into larger sub-assemblies which can be invested, burnt-out and cast in metal. The large, metal sub-assemblies may then be welded together into the finished designs with a total size larger than the capability of either the Stereolithography apparatus or the foundry.

Genus 1, Infinite-Ended Minimal Surface Including a Topological Handle, 24" x 16" x 16", Wax, (c) 1999 David Hoffman, Stewart Dickson.

Genus 1, Infinite-Ended Minimal Surface Including a Topological Handle, 24" x 16" x 16", Wax, (c) 1999 David Hoffman, Stewart Dickson.

Genus 1, Infinite-Ended Minimal Surface Including a Topological Handle, 24" x 16" x 16", Wax, (c) 1999 David Hoffman, Stewart Dickson.

Software/Hardware used: Mathematical form discovered using Visual Programming Language (VPL) by James Hoffman on a Ridge 32/110 computer with Raster Technologies One/380 graphics controller. Database adapted for sculpture by Stewart Dickson using original C-language enhancements to the Wavefront modeling environment on a Silicon Graphics IRIS 3030. Stereolithography by Hughes Aircraft Company, El Segundo, CA, funding by ACM/SIGGRAPH Special Projects Committee, T. Defanti, Chair.

Costa's Genus 1, 3-Ended Minimal Surface, Mathematica stereoscopic computer visualization, (c) 1990 Stewart Dickson.

Press Here for PostScript text on the mathmatics of minimal surfaces.

Software/Hardware used: The Mathematica system for doing mathematics by computer. Silicon Graphics 4D/25TG Personal Iris.

MPEG Movie of Torus-to-Costa Homotopy (40587 bytes) (531 kByte QuickTime) (c) 1990 Stewart Dickson.

Software/Hardware used: The Mathematica system for doing mathematics by computer. Silicon Graphics 4D/25TG Personal Iris.

Quicktime movie of a proposal for a 3-D Zoetrope based on the homotopy of a simple torus metamorphosing into the genus 1, three-ended minimal surface. See the full proposal and construction documentation here.

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