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Meeting Alhambra, Granada 2003Meeting Alhambra, Granada 2003
“Whirled White Web”
Art and Math in Snow
Carlo H. Séquin
Brent Collins, Steve Reinmuth
Dan Schwalbe, Stan Wagon
Scherk’s 2nd Minimal SurfaceScherk’s 2nd Minimal Surface
Normal“biped”saddles
Generalization to higher-order saddles(monkey saddle)
““Hyperbolic Hexagon” by B. CollinsHyperbolic Hexagon” by B. Collins
6 saddles in a ring
6 holes passing through symmetry plane at ±45º
= “wound up” 6-story Scherk tower
Discussion: What if … we added more stories ?
or introduced a twist before closing the ring ?
Brent Collins’ Prototyping ProcessBrent Collins’ Prototyping Process
Armature for the "Hyperbolic Heptagon"
Mockup for the "Saddle Trefoil"
Time-consuming ! (1-3 weeks)
Collins’ Fabrication ProcessCollins’ Fabrication Process
Example: “Vox Solis”
Layered laminated main shapeWood master pattern
for sculpture
Slices through “Minimal Trefoil”Slices through “Minimal Trefoil”
50% 10%23%30%
45% 5%20%27%
35% 2%15%25%
One thick slicethru sculpture,from which Brent can cut boards and assemble a rough shape.
Traces represent: top and bottom,as well as cuts at 1/4, 1/2, 3/4of one board.
Profiled Slice through “Heptoroid”Profiled Slice through “Heptoroid”
Hyper-Sculpture: “Family of 12 Trefoils”Hyper-Sculpture: “Family of 12 Trefoils”
W=2
W=1
B=1 B=2 B=3 B=4
Stan Wagon, Stan Wagon, Macalester College, St. Paul, MNMacalester College, St. Paul, MN
Leader of Team “USA – Minnesota”
Breckenridge, Breckenridge, 20022002
Bathsheba Grossman:
“A Twist in Time”
Honorable Mention
“Expressive Impact”
Snow-Sculpting, Breckenridge, 2003Snow-Sculpting, Breckenridge, 2003
Brent Collins and Carlo Séquin
are invited to join the team
and to provide a design.
Other Team Members:
Stan Wagon, Dan Schwalbe, Steve Reinmuth
(= Team “Minnesota”)
Collins’ Initial Suggestion: Minimal TrefoilCollins’ Initial Suggestion: Minimal Trefoil
Stan’s Objection: “Too simple …– we know we can do this.
No risk – no fun !”
Name, StoryName, Story
“Snow Flower, Winter Rose, Winter Whirl, Wild White Whirl, Webbed Wild Whirl, Whirled Wild Web …”
finally the perfect homonym:
“Whirled White Web”
Like this global network, the ridges of our sculpture span the outer perimeters of the whole “globe,” and at the same time come close together in the central hole. It illustrates how the WWW can link together people from all over the world.
Plan of AttackPlan of Attack
Cut away 2 large triangular prisms;
Hang plastic template (12’x18’) over slab;
Mark projections of holes, flanges;
Drill, carve, refine …(using maquette for reference)
Try this first on a smaller practice block!
The WinnersThe Winners
1st: Canada – B.C., 2nd: USA – Minnesota, 3rd: USA – Breckenridge
“… sacred geometry … very intricate … very 21st century !”
What Are We Going To Do For 2004 ?What Are We Going To Do For 2004 ?
“Turning a Snowball Inside Out”
Sphere EversionSphere Eversion
~ 1960, the blind mathematician B. Morin, (born 1931) conceived of a way how a sphere can be turned inside-out:
Surface may pass through itself,
but no ripping, puncturing, creasing allowed,e.g., this is not an acceptable solution:
PINCH
Morin SurfaceMorin Surface But there are more contorted paths
that can achieve the desired goal.
The Morin surface is the half-way point of one such path:
John Sullivan: “The Optiverse”
Simplest ModelSimplest Model
Partial cardboard model based on the simplest polyhedral sphere (= cuboctahedron) eversion.
Gridded Models for TransparencyGridded Models for Transparency
3D-Print from Zcorp SLIDE virtual model
Shape Adaption for Snow SculptureShape Adaption for Snow Sculpture
Restructured Morin surface to fit block size: (10’ x 10’ x 12’)
Make Surface “Transparent”Make Surface “Transparent”
Realize surface as a grid.
Draw a mesh of smooth lines onto the surface …
““Turning a Snowball Inside-Out”Turning a Snowball Inside-Out”
Carlo H. Séquin, Alex Kozlowski, John Sullivan
Dan Schwalbe, Stan Wagon