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LASER, December 10, 2014

Explore the 20-year collaboration between Brent Collins and Carlo H. Séquin, focused on innovative topological art designs. Discover the fascinating mathematical concepts behind Collins' sculptures, from logarithmic spirals to knot-spanning surfaces. Dive into the prototyping and fabrication processes that bring these intricate designs to life.

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LASER, December 10, 2014

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  1. LASER, December 10, 2014 "Hyperbolic Hexagon" to "Evolving Trefoil“ my 20-year collaboration with Brent Collins Carlo H. Séquin University of California, Berkeley

  2. Basel, Switzerland M N G

  3. Logarithmic Spiral Jakob Bernoulli (1654‒1705)

  4. Leonhard Euler (1707‒1783) Imaginary Numbers

  5. Geometry in every assignment . . . CCD TV Camera (1973) Soda Hall (1992) RISC 1 MicroChip (1982) Octa-Gear (2000)

  6. Recent Designs and Models

  7. Leonardo -- Special Issue On Knot-Spanning Surfaces: An Illustrated Essay on Topological Art With an Artist’s Statement by Brent Collins George K. Francis with Brent Collins

  8. More Sculptures by Brent Collins Photos by Phillip Geller

  9. The Math in Collins’ Sculptures • Collins works with rulers and compasses;any math in his early work is intuitive. • He is inspired by nature,e.g. soap films (= minimal area surfaces)(& minimal bending, too). • George Francis analyzed Collins’ sculpturesin terms of the knots formed by their rimsand the topology of the spanning surfaces. • Let’s look at the local geometry found oftenin these tunnel & saddle surfaces: 

  10. Scherk’s 2nd Minimal Surface (1834) Normal “biped” saddles 2 planes:  bi-ped saddles “Scherk Tower”

  11. “Hyperbolic Hexagon”by Brent Collins • 6 saddles in a ring . . . • = “wound up” (toroidal)6-story Scherk tower. • 6 holes passing through symmetry plane at ±45º • Discussion: What if … • we added more stories ? • or introduced a twist before closing the ring ?

  12. Closing the Loop straight or twisted “Scherk Tower” “Scherk-Collins Toroids”

  13. Brent Collins’ Prototyping Process Bees wax Mockup for the "Saddle Trefoil" Armature for the "Hyperbolic Heptagon”(7 Scherk stories) Time-consuming ! (1-2 weeks)

  14. Sculpture Generator 1, GUI

  15. Shapes from Sculpture Generator 1

  16. Brent Collins, 1997 “Hyperbolic Hexagon II”

  17. Collins’ Fabrication Process Wood master patternfor sculpture Layered laminated main shape Example: Vox Solis

  18. Profiled Slice through “Heptoroid” • 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.

  19. Emergence of the Heptoroid (1) Assembly of the precut boards

  20. Emergence of the Heptoroid (2) Forming a continuous smooth edge

  21. Emergence of the Heptoroid (3) Smoothing the whole surface

  22. The Finished Heptoroid • at Fermi Lab Art Gallery (1998).

  23. 2003: “Whirled White Web”

  24. 12:40 pm -- 42° F

  25. 12:41 pm -- 42° F

  26. “WWW” Wins Silver Medal

  27. 12-Story Scherk-Collins Toroid • branches = 4 • storeys = 11 • height = 1.55 • flange = 1.00 • thickness = 0.06 • rim_bulge = 1.00 • warp = 330.00 • twist = 247.50 • azimuth = 56.25 • mesh_tiles = 0 • textr_tiles = 1 • detail = 8 • bounding box: • xmax= 6.01, • ymax= 1.14, • zmax= 5.55, • xmin= -7.93, • ymin= -1.14, • zmin= -8.41

  28. 12 Signs of the Zodiac

  29. David Lynn, Nova Blue Studio Arts • http://sites.google.com/site/novabluestudioarts/

  30. Master Module for “Millennium Arch”

  31. Fabrication of “Millennium Arch” The mold for the key module A polyester segment cast

  32. Two Times Three Modules

  33. Merging the Two Half-Circles

  34. Brent Collins and David Lynn

  35. “Millennium Arch” by Night

  36. Millennium ManVitruvian Manby Leonardo

  37. Concept of “Evolving Trefoil” New: Let a hole-saddle chain follow an arbitrary space curve!

  38. Sculpture Generator #2

  39. An Evolution of Ideas and Forms

  40. 3 of 6 Maquette Modules (FDM)(after cleaning away support)

  41. Full-Size Master Module and Mold About 20 fiberglass pieces bolted together Milled foam core coated with clay

  42. Formation of a Main Sculpture Module

  43. Sealed-off Mold (Catalyzed Matrix Inside)

  44. Fabricate 6 Identical Pieces • 6 identical pieces had to be fabricated in this labor-intensive way!

  45. Three Units at Nova Blue Studio Arts

  46. Installation at MWSU, Feb. 2013

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