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CONTACT, March. 21-23, 2003. Art, Math, Computers, and Creativity. Carlo Séquin, University of California, Berkeley. I am a Designer …. CCD Camera, Bell Labs, 1973 Soda Hall, Berkeley, 1994. RISC chip, Berkeley, 1981 “Octa-Gear”, Berkeley, 2000. Focus of Talk.

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CONTACT, March. 21-23, 2003

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CONTACT, March. 21-23, 2003

Art, Math, Computers,

and Creativity

Carlo Séquin,

University of California, Berkeley


I am a Designer …

CCD Camera, Bell Labs, 1973 Soda Hall, Berkeley, 1994

RISC chip, Berkeley, 1981 “Octa-Gear”, Berkeley, 2000


Focus of Talk

The role of the computer in:

  • aesthetic optimization,

  • the creative process.


Brent Collins

“Hyperbolic Hexagon II”


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


Brent Collins: Stacked Saddles


Scherk’s 2nd Minimal Surface

Normal

“biped”

saddles

Generalization to

higher-order saddles(monkey saddle)


“Hyperbolic Hexagon” by B. Collins

  • 6 saddles in a ring

  • 6 holes passing through symmetry plane at ±45º

  • “wound up” 6-story Scherk tower

  • What would happen,

    • if we added more stories ?

    • or introduced a twist before closing the ring ?


Closing the Loop

straight

or

twisted


Brent Collins’ Prototyping Process

Mockup for the "Saddle Trefoil"

Armature for the "Hyperbolic Heptagon"

Time-consuming ! (1-3 weeks)


“Sculpture Generator I”, GUI


A Simple Scherk-Collins Toroid

Parameters:(genome)

  • branches = 2

  • stories = 1

  • height = 5.00

  • flange = 1.00

  • thickness = 0.10

  • rim_bulge = 1.00

  • warp = 360.00

  • twist = 90

  • azimuth = 90

  • textr_tiles = 3

  • detail = 8


A Scherk Tower (on its side)

  • branches = 7

  • stories = 3

  • height = 0.2

  • flange = 1.00

  • thickness = 0.04

  • rim_bulge = 0

  • warp = 0

  • twist = 0

  • azimuth = 0

  • textr_tiles = 2

  • detail = 6


1-story Scherk Tower

  • branches = 5

  • stories = 1

  • height = 1.35

  • flange = 1.00

  • thickness = 0.04

  • rim_bulge = 0

  • warp = 58.0

  • twist = 37.5

  • azimuth = 0

  • textr_tiles = 8

  • detail = 6


180º Arch = Half a Scherk Toroid

  • branches = 8

  • stories = 1

  • height = 5

  • flange = 1.00

  • thickness = 0.06

  • rim_bulge = 1.25

  • warp = 180

  • twist = 0

  • azimuth = 0

  • textr_tiles = e

  • detail = 12


V-art

VirtualGlassScherkTowerwith

MonkeySaddles(Radiance 40 hours)

Jane Yen


How to Obtain a Real Sculpture ?

  • Prepare a set of cross-sectional blue printsat equally spaced height intervals,corresponding to the board thicknessthat Collins is using for the construction.


Collins’ Fabrication Process

Wood master patternfor sculpture

Layered laminated main shape

Example: “Vox Solis”


Slices through “Minimal Trefoil”

50%

30%

23%

10%

45%

27%

20%

5%

35%

25%

15%

2%


Profiled Slice through the Sculpture

  • One thick slicethru “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, 3/4of one board.


Emergence of the “Heptoroid” (1)

Assembly of the precut boards


Emergence of the “Heptoroid” (2)

Forming a continuous smooth edge


Emergence of the “Heptoroid” (3)

Smoothing the whole surface


The Finished “Heptoroid”

  • at Fermi Lab Art Gallery (1998).


SFF (Solid Free-form Fabrication)

Monkey-

Saddle

Cinquefoil


Fused Deposition Modeling (FDM)


Zooming into the FDM Machine


Various “Scherk-Collins” Sculptures


Part II

Developing

Parameterized

Sculpture Families

(Extending a Paradigm)


Family of Symmetrical Trefoils

W=2

W=1

B=1 B=2 B=3 B=4


Close-up of Some Trefoils

B=1 B=2 B=3

Varying the number of branches, the order of the saddles.


Higher-order Trefoils (4th order saddles)

W=1 (Warp)

W=2 


Exploring New Ideas: W=2

  • Going around the loop twice ...

… resulting in an interwoven structure.


9-story Intertwined Double Toroid

Bronze

investment

casting fromwax original made on3D Systems’“Thermojet”


Stepwise Expansion of Horizon

  • Playing with many different shapes and

  • experimenting at the limit of the domain of the sculpture generator,

  • stimulates new ideas for alternative shapes and generating paradigms.

Swiss Mountains


Note:

The computer becomesan amplifier / acceleratorfor the creative process.


Séquin’s “Minimal Saddle Trefoil”

  • bronze cast, gold plated


Minimal Trefoils -- cast and finished by Steve Reinmuth


Steve Reinmuth


Brent Collins’ “Pax Mundi”

A new inspiration


Keeping up with Brent ...

  • Sculpture Generator Ican only do warped Scherk towers,not able to describe a shape like Pax Mundi.

  • Need a more general approach !

  • Use the SLIDE modeling environment(developed at U.C. Berkeley by J. Smith)to capture the paradigm of such a sculpturein a procedural form.

    • Express it as a computer program

    • Insert parameters to change salient aspects / features of the sculpture

    • First: Need to understand what is going on 


Part III

The “Least Understood” Step

(Capturing a Paradigm)


Sculptures by Naum Gabo

Pathway on a sphere:

Edge of surface is like seam of tennis ball;

 2-period Gabo curve.


2-period Gabo Curve

  • Approximation with quartic B-splinewith 8 control points per period,but only 3 DOF are used.


4-period Gabo Curve

Same construction as for a 2-period curve


“Pax Mundi” Revisited

  • Can be seen as:Amplitude modulated, 4-period Gabo curve


SLIDE-UI for “Pax Mundi” Shapes


“Viae Globi” Family (Roads on a Sphere)

L2 L3 L4 L5


Via Globi 3 (Stone)

Wilmin Martono


Via Globi 5 (Wood)

Wilmin Martono


Extending the Paradigm

Try to Expand the Sculpture Family:

  • Aim for more highly convoluted paths,

  • maintain high degree of symmetry.

  • Need a better tool to draw on sphere …


Circle Splines on the Sphere

Examples from Jane Yen’s Editor Program

(= another piece of “scaffolding”)


Via Globi -- Virtual Design

Wilmin Martono


“Maloja”(FDM part)

  • A rather winding Swiss mountain pass road in the upper Engadin.


“Stelvio”

  • An even more convoluted alpine pass in Italy.


“Altamont”

  • Celebrating American multi-lane highways.


“Lombard”

  • A very famous crooked street in San Francisco

  • Note that I switched to a flat ribbon.


Part IV

How to make a really large sculpture ?

  • Scaling-up problems

  • Production problems

  • Engineering problems

  • Installation problems

  • Maintenance problems

  • Insurance problems

     Need a Commission !


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


Stan Wagon, Macalester College, St. Paul, MN

  • Leader of Team “USA – Minnesota”


Breckenridge, 1999

Helaman Ferguson: “Invisible Handshake”


Breckenridge, 2000

Robert Longhurst:

“Rhapsody in White”

2nd Place


Breckenridge, 2002

Bathsheba Grossman:

“A Twist in Time”

Honorable Mention

“Expressive Impact”


Monkey Saddle Trefoil

from Sculpture Generator I


Maquettes

3D-Print FDM


Name, 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.


ACCEPTED !

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


Construction Drawings

Top View Side View Axial View

Remove these prisms first!


Day 1

Removing lot’s of snow …


Day 1: The “Monolith”

Cut away prisms …


Day 2: Making a Torus

Mark center, circles … Bull’s-eye !


Chipping away …


End of Day 2

The Torus


Day 3, am: Drawing Flanges


Day 3, pm: Flanges, Holes


Day 4: Geometry Refinement


End of Day 4: Desired Geometry


Day 5, am: Surface Refinement


“House Cleaning”


“Whirled White Web”


Official Team Photo


Part V

DISCUSSION:

How much of this process could have been done by a computer alone

?


The Starting Point

  • In many instances my work started from one of Brent Collins’ sculptures.

  • Where did Brent get his ideas from ?( “Forms found in nature” )

  • 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.


Capturing a Paradigm

  • What made me think of Naum Gabo, when I tried to understand Collin’s “Pax Mundi”?

  • How did I know that it was a good match ?

     I needed to understand:

    • It is a sweep,

    • Path lies on a sphere and

    • has some regularity to its undulations


Extending a Paradigm

  • 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.

  • It takes some “informed judgment” to decide which ones will actually work as parameters, and what their useful value range should be.

  • Also, when is it appropriate / productive to extend the range of a parameter?


Is It Art ?

  • Can it be art, -- if it is created by a computer ?

  • Who judges which parameters to pick ?-- what are “successful” combinations ?

  • How many cultures (today & in the future) would recognize these shapes as being something special ?


QUESTIONS ?DISCUSSION ?


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