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Color 3-D Prints

by Stewart Dickson

Color Studies of Enneper's Minimal Surface

Computer Rendering of Enneper's Surface Computer Rendering of Enneper's Surface The Gauss Map of a surface associates to each
point on the surface its unit
normal vector.


In these studies, the Unit Normals
to the surface are used to create a color mapping on the surface
which imitates the default Mathematica
(lighting)/rendering model. 


LightSources
  {{{1.,0.,1.},RGBColor[1,0,0]},{{1.,1.,1.},
      RGBColor[0,1,0]},{{0.,1.,1.},RGBColor[0,0,1]}}

In these studies, however, the color calculations are done in CMY color space and the background is white.

Stewart Dickson has written the software to convert the Gauss-map of an object to a Mathematica-style surface color map. Download here.

See also Computer-Generated Bronze Sculpture

Color Snakeskin Texture-Mapped Trefoil Torus Knot

Computer Rendering: Green Snake Torus Knot Physical 3-D Color Print: Green Snake Torus Knot

The texture image is parametrically
mapped along the knotted torus.


Color 3-D Printing was done by Z Corporation. Download here.




Logarithmic Spiral Snail

Computer Rendering: Snail Shell Computer Rendering: Snail Shell

A snail shell generated in Mathematica Download here.


See also Computer-Generated Bronze Sculpture







HyperCosta Surface

Computer Rendering of HyperCosta Surface Physical 3D Print of HyperCosta Surface A Hypothetical Hyperspace extension
of Costa's Minimal Surface.









Fermat's Last Theorem

Computer Rendering: N=5 Fermat Surface The Seventeenth-Century French mathematician Pierre de Fermat wrote in the margin of his copy of Arithmetica by Diophantus, near the section on the Pythagorean Theorem (a squared plus b squared equals c squared),
"x ^ n + y ^ n = z ^ n - it cannot be solved with non-zero integers x, y, z for any exponent n greater than 2. I have found a truly marvelous proof, which this margin is too small to contain."
This was left as an enigmatic riddle after Fermat's death and it became a famous, unsolved problem of number theory for over 350 years.

Andrew Hanson has made some pictures, and I have in turn made sculpture, of a system analogous to Fermat's last theorem - a superquadric surface parameterized in complex four-space.

We think that the mathematics of the n=3 case are similar to Fermat's own proof of the n=3 special case. Our pictures have lent some visual concreteness to the recent news of Andrew Wiles' proof of the Taniyama-Weil conjecture, which implies the proof of Fermat.

Physical 3-D Color Print: N=5 Fermat Surface See also the Proposal for A Three-Dimensional Zoetrope

3-D Fractals

Computer-Rendered 3-D Julia Fractal The Z Corporation 3-D Color Printer has a Bit-Mapped, color image slice-based software interface to its build process. This interface makes the Z Corp machine the ideal platform on which to execute the Fractal Zoom in Three Physical Dimensions -- and in color!

Stewart Dickson has written the software to interface this data object to the Z Corp 3-D Color Printer. Download here.























Painted Vases

Computer Rendering: Vase with Klimt's Emilie Computer Rendering: Vase with Seurat's Grande Jatte The artist has developed the
software to generate a Vase,
as a mathematical function,
and to map a color digital
image onto the surface as a
VRML V2.0 file.



This file format is suitable
for output using the Z Corp
Color 3-D Printer. Download here.



Computer Rendering: Vase with Red Nude

"Botty Shelly"

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