1. CONTACT, March. 21-23, 2003 Art, Math, Computers, and Creativity Carlo Séquin, University of California, Berkeley

2. I am a Designer … CCD Camera, Bell Labs, 1973 Soda Hall, Berkeley, 1994 RISC chip, Berkeley, 1981 “Octa-Gear”, Berkeley, 2000

3. Focus of Talk The role of the computer in: u aesthetic optimization, u the creative process.

4. Brent Collins “Hyperbolic Hexagon II”

5. 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

6. Brent Collins: Stacked Saddles

7. Scherk’s 2nd Minimal Surface Normal “biped” saddles Generalization to higher-order saddles (monkey saddle)

8. “Hyperbolic Hexagon” by B. Collins u 6 saddles in a ring u 6 holes passing through symmetry plane at ±45º u “wound up” 6-story Scherk tower u What would happen, l if we added more stories ? l or introduced a twist before closing the ring ?

9. Closing the Loop straight or twisted

10. Brent Collins’ Prototyping Process Armature for the "Hyperbolic Heptagon" Mockup for the "Saddle Trefoil" Time-consuming ! (1-3 weeks)

11. “Sculpture Generator I”, GUI

12. A Simple Scherk-Collins Toroid Parameters: (genome) u branches = 2 u stories = 1 u height = 5.00 u flange = 1.00 u thickness = 0.10 u rim_bulge = 1.00 u warp = 360.00 u twist = 90 u azimuth = 90 u textr_tiles = 3 u detail = 8

13. A Scherk Tower (on its side) u branches = 7 u stories = 3 u height = 0.2 u flange = 1.00 u thickness = 0.04 u rim_bulge = 0 u warp = 0 u twist = 0 u azimuth = 0 u textr_tiles = 2 u detail = 6

14. 1-story Scherk Tower u branches = 5 u stories = 1 u height = 1.35 u flange = 1.00 u thickness = 0.04 u rim_bulge = 0 u warp = 58.0 u twist = 37.5 u azimuth = 0 u textr_tiles = 8 u detail = 6

15. 180º Arch = Half a Scherk Toroid u branches = 8 u stories = 1 u height = 5 u flange = 1.00 u thickness = 0.06 u rim_bulge = 1.25 u warp = 180 u twist = 0 u azimuth = 0 u textr_tiles = e u detail = 12

16. V-art Virtual Glass Scherk Tower with Monkey Saddles (Radiance 40 hours) Jane Yen

17. How to Obtain a Real Sculpture ? u Prepare a set of cross-sectional blue prints at equally spaced height intervals, corresponding to the board thickness that Collins is using for the construction.

18. Collins’ Fabrication Process Example: “Vox Solis” Layered laminated main shape Wood master pattern for sculpture

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

20. u One thick slice thru “Heptoroid” 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, 3/4 of one board. Profiled Slice through the Sculpture

21. Emergence of the “Heptoroid” (1) Assembly of the precut boards

22. Emergence of the “Heptoroid” (2) Forming a continuous smooth edge

23. Emergence of the “Heptoroid” (3) Smoothing the whole surface

24. The Finished “Heptoroid” u at Fermi Lab Art Gallery (1998).

25. SFF (Solid Free-form Fabrication) Monkey- Saddle Cinquefoil

26. Fused Deposition Modeling (FDM)

27. Zooming into the FDM Machine

28. Various “Scherk-Collins” Sculptures

29. Part II Developing Parameterized Sculpture Families (Extending a Paradigm)

30. Family of Symmetrical Trefoils W=2 W=1 B=1 B=2 B=3 B=4

31. Close-up of Some Trefoils B=1 B=2 B=3 Varying the number of branches, the order of the saddles.

32. Higher-order Trefoils (4th order saddles) W=1 (Warp)W=2 

33. Exploring New Ideas: W=2 u Going around the loop twice... … resulting in an interwoven structure.

34. 9-story Intertwined Double Toroid Bronze investment casting from wax original made on 3D Systems’ “Thermojet”

35. Stepwise Expansion of Horizon u Playing with many different shapes and u experimenting at the limit of the domain of the sculpture generator, u stimulates new ideas for alternative shapes and generating paradigms. Swiss Mountains

36. Note: The computer becomes an amplifier / accelerator for the creative process.

37. Séquin’s “Minimal Saddle Trefoil” u bronze cast, gold plated

38. Minimal Trefoils -- cast and finished by Steve Reinmuth

39. Steve Reinmuth

40. Brent Collins’ “Pax Mundi” A new inspiration

41. Keeping up with Brent... u Sculpture Generator I can only do warped Scherk towers, not able to describe a shape like Pax Mundi. u Need a more general approach ! u Use the SLIDE modeling environment (developed at U.C. Berkeley by J. Smith) to capture the paradigm of such a sculpture in a procedural form. l Express it as a computer program l Insert parameters to change salient aspects / features of the sculpture l First: Need to understand what is going on 

42. Part III The “Least Understood” Step (Capturing a Paradigm)

43. Sculptures by Naum Gabo Pathway on a sphere: Edge of surface is like seam of tennis ball;  2-period Gabo curve.

44. 2-period Gabo Curve u Approximation with quartic B-spline with 8 control points per period, but only 3 DOF are used.

45. 4-period Gabo Curve Same construction as for a 2-period curve

46. “Pax Mundi” Revisited u Can be seen as: Amplitude modulated, 4-period Gabo curve

47. SLIDE-UI for “Pax Mundi” Shapes

48. “Viae Globi” Family (Roads on a Sphere) L2 L3 L4 L5

49. Via Globi 3 (Stone) Wilmin Martono

50. Via Globi 5 (Wood) Wilmin Martono

51. Extending the Paradigm Try to Expand the Sculpture Family: u Aim for more highly convoluted paths, u maintain high degree of symmetry. u Need a better tool to draw on sphere …

52. Circle Splines on the Sphere Examples from Jane Yen’s Editor Program (= another piece of “scaffolding”)

53. Via Globi -- Virtual Design Wilmin Martono

54. “Maloja” (FDM part) u A rather winding Swiss mountain pass road in the upper Engadin.

55. “Stelvio” u An even more convoluted alpine pass in Italy.

56. “Altamont” u Celebrating American multi-lane highways.

57. “Lombard” u A very famous crooked street in San Francisco u Note that I switched to a flat ribbon.

58. Part IV How to make a really large sculpture ? u Scaling-up problems u Production problems u Engineering problems u Installation problems u Maintenance problems u Insurance problems  Need a Commission !

59. International Snow-sculpting Championships, Breckenridge, 2003 Brent Collins and Carlo Séquin are invited to provide a design for Team “USA – Minnesota” Other Team Members: Stan Wagon, Dan Schwalbe, Steve Reinmuth

60. Stan Wagon, Macalester College, St. Paul, MN u Leader of Team “USA – Minnesota”

61. Breckenridge, 1999 Helaman Ferguson: “Invisible Handshake”

62. Breckenridge, 2000 Robert Longhurst: “Rhapsody in White” 2 nd Place

63. Breckenridge, 2002 Bathsheba Grossman: “A Twist in Time” Honorable Mention “Expressive Impact”

64. Monkey Saddle Trefoil from Sculpture Generator I

65. Maquettes 3D-Print FDM

66. Name, Story u “Snow Flower, Winter Rose, Winter Whirl, Wild White Whirl, Webbed Wild Whirl, Whirled Wild Web …” u finally the perfect homonym: “Whirled White Web” u 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.

67. ACCEPTED ! Now – how do we get this design into a 10’x10’x12’ block of snow ?

68. Construction Drawings Top View Side View Axial View Remove these prisms first!

69. Removing lot’s of snow … Day 1

70. Day 1: The “Monolith” Cut away prisms …

71. Day 2: Making a Torus Mark center, circles … Bull’s-eye !

73. Chipping away …

74. End of Day 2 The Torus

75. Day 3, am: Drawing Flanges

76. Day 3, pm: Flanges, Holes

77. Day 4: Geometry Refinement

79. End of Day 4: Desired Geometry

80. Day 5, am: Surface Refinement

81. “House Cleaning”

82. “Whirled White Web”

84. Official Team Photo

85. Part V DISCUSSION: How much of this process could have been done by a computer alone ?

86. The Starting Point u In many instances my work started from one of Brent Collins’ sculptures. u Where did Brent get his ideas from ? (  “Forms found in nature” ) u How soon will we able to say: “Computer, make me something like that !” “Make me a few more in the same style !” (1) Capturing a Paradigm. (2) Extending a Paradigm.

87. Capturing a Paradigm u What made me think of Naum Gabo, when I tried to understand Collin’s “Pax Mundi”? u How did I know that it was a good match ?  I needed to understand: l It is a sweep, l Path lies on a sphere and l has some regularity to its undulations

88. Extending a Paradigm u A paradigm expressed, so that a computer can deal with it, is typically an “algorithm”; and this program will have some variables, some of which can be used as parameters. u It takes some “informed judgment” to decide which ones will actually work as parameters, and what their useful value range should be. u Also, when is it appropriate / productive to extend the range of a parameter?

89. Is It Art ? u Can it be art, -- if it is created by a computer ? u Who judges which parameters to pick ? -- what are “successful” combinations ? u How many cultures (today & in the future) would recognize these shapes as being something special ?

90. QUESTIONS ? DISCUSSION ?