CONTACT, March. 21-23, 2003CONTACT, March. 21-23, 2003

Art, Math, Computers,

and Creativity

Carlo Séquin,

University of California, Berkeley

I am a Designer …I am a Designer …

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

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

Focus of TalkFocus of Talk

The role of the computer in:

aesthetic optimization,

the creative process.

Brent CollinsBrent Collins

“Hyperbolic Hexagon II”

Leonardo -- Special IssueLeonardo -- Special Issue

On Knot-Spanning Surfaces: An Illustrated Essay on Topological ArtWith an Artist’s Statement by Brent Collins

George K. Francis with Brent Collins

Brent Collins: Stacked SaddlesBrent Collins: Stacked Saddles

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

What would happen, if we added more stories ?

or introduced a twist before closing the ring ?

Closing the LoopClosing the Loop

straight

or

twisted

Brent Collins’ Prototyping ProcessBrent Collins’ Prototyping Process

Armature for the "Hyperbolic Heptagon"

Mockup for the "Saddle Trefoil"

Time-consuming ! (1-3 weeks)

““Sculpture Generator I”, GUI Sculpture Generator I”, GUI

A Simple Scherk-Collins ToroidA 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 A Scherk Tower (on its side)(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 Tower1-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 Toroid180º 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-artV-art

VirtualGlassScherkTowerwithMonkeySaddles

(Radiance 40 hours)

Jane Yen

How to Obtain a How to Obtain a RealReal Sculpture ? Sculpture ?

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.

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 “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.

Profiled Slice through the SculptureProfiled Slice through the Sculpture

Emergence of the “Heptoroid” (1)Emergence of the “Heptoroid” (1)

Assembly of the precut boards

Emergence of the “Heptoroid” (2)Emergence of the “Heptoroid” (2)

Forming a continuous smooth edge

Emergence of the “Heptoroid” (3)Emergence of the “Heptoroid” (3)

Smoothing the whole surface

The Finished The Finished “Heptoroid”“Heptoroid”

at Fermi Lab Art Gallery (1998).

SFF (Solid Free-form Fabrication)SFF (Solid Free-form Fabrication)

Monkey-SaddleCinquefoil

Fused Deposition Modeling (FDM)Fused Deposition Modeling (FDM)

Zooming into the FDM MachineZooming into the FDM Machine

Various “Scherk-Collins” SculpturesVarious “Scherk-Collins” Sculptures

Part IIPart II

Developing Parameterized

Sculpture Families

(Extending a Paradigm)

Family of Symmetrical TrefoilsFamily of Symmetrical Trefoils

W=2

W=1

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

Close-up of Some TrefoilsClose-up of Some Trefoils

B=1 B=2 B=3

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

Higher-order Trefoils Higher-order Trefoils (4th order saddles)(4th order saddles)

W=1 (Warp) W=2

Exploring New Ideas: W=2Exploring New Ideas: W=2

Going around the loop twice ...

… resulting in an interwoven structure.

9-story Intertwined Double Toroid9-story Intertwined Double Toroid

Bronzeinvestment casting from wax original made on 3D Systems’“Thermojet”

Stepwise Expansion of HorizonStepwise 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:Note:

The computer becomesan amplifier / acceleratorfor the creative process.

Séquin’s “Minimal Saddle Trefoil”Séquin’s “Minimal Saddle Trefoil”

bronze cast, gold plated

Minimal Trefoils -- cast and Minimal Trefoils -- cast and finished by Steve Reinmuthfinished by Steve Reinmuth

Steve ReinmuthSteve Reinmuth

Brent Collins’ Brent Collins’

“Pax Mundi”“Pax Mundi”

A new inspiration

Keeping up with Brent ...Keeping up with Brent ...

Sculpture Generator I can 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 IIIPart III

The “Least Understood” Step

(Capturing a Paradigm)

Sculptures by Naum GaboSculptures by Naum Gabo

Pathway on a sphere:

Edge of surface is like seam of tennis ball;

2-period Gabo curve.

2-period Gabo Curve2-period Gabo Curve

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

4-period Gabo Curve4-period Gabo Curve

Same construction as for a 2-period curve

““Pax Mundi” RevisitedPax Mundi” Revisited

Can be seen as:

Amplitude modulated, 4-period Gabo curve

SLIDE-UI for “Pax Mundi” ShapesSLIDE-UI for “Pax Mundi” Shapes

““Viae Globi” Family Viae Globi” Family (Roads on a Sphere)(Roads on a Sphere)

L2 L3 L4 L5

Via Globi 3 (Stone)Via Globi 3 (Stone)

Wilmin Martono

Via Globi 5 (Wood)Via Globi 5 (Wood)

Wilmin Martono

Extending the ParadigmExtending 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 SphereCircle Splines on the Sphere

Examples from Jane Yen’s Editor Program

(= another piece of “scaffolding”)

Via Globi -- Virtual DesignVia Globi -- Virtual Design

Wilmin Martono

““Maloja”Maloja” (FDM part)(FDM part)

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

““Stelvio”Stelvio”

An even more convoluted alpine pass in Italy.

““Altamont”Altamont”

Celebrating American multi-lane highways.

““Lombard”Lombard”

A very famous crooked street in San Francisco

Note that I switched to a flat ribbon.

Part IVPart 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 International Snow-sculpting Championships, Breckenridge, 2003Championships, 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, Stan Wagon, Macalester College, St. Paul, MNMacalester College, St. Paul, MN

Leader of Team “USA – Minnesota”

Breckenridge, 1999Breckenridge, 1999

Helaman Ferguson: “Invisible Handshake”

Breckenridge, Breckenridge, 20002000

Robert Longhurst:

“Rhapsody in White”

2nd Place

Breckenridge, Breckenridge, 20022002

Bathsheba Grossman:

“A Twist in Time”

Honorable Mention

“Expressive Impact”

Monkey Saddle TrefoilMonkey Saddle Trefoil

from Sculpture Generator I

MaquettesMaquettes

3D-Print FDM

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.

ACCEPTED !ACCEPTED !

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

Construction DrawingsConstruction Drawings

Top View Side View Axial View

Remove these prisms first!

Removing lot’s of snow …

Day 1Day 1

Day 1: The “Monolith”Day 1: The “Monolith”

Cut away prisms …

Day 2: Making a TorusDay 2: Making a Torus

Mark center, circles … Bull’s-eye !

Chipping away …Chipping away …

End of Day 2End of Day 2

The Torus

Day 3, am: Drawing FlangesDay 3, am: Drawing Flanges

Day 3, pm: Flanges, Holes Day 3, pm: Flanges, Holes

Day 4: Geometry RefinementDay 4: Geometry Refinement

End of Day 4: Desired GeometryEnd of Day 4: Desired Geometry

Day 5, am: Surface RefinementDay 5, am: Surface Refinement

““House Cleaning”House Cleaning”

““Whirled White Web”Whirled White Web”

Official Team PhotoOfficial Team Photo

Part VPart V

DISCUSSION:

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

?

The Starting PointThe 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 ParadigmCapturing 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 ParadigmExtending 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 ?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 ?QUESTIONS ?

DISCUSSION ?DISCUSSION ?