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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

CONTACT, 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 talk

Focus of Talk

The role of the computer in:

  • aesthetic optimization,

  • the creative process.

Brent collins

Brent Collins

“Hyperbolic Hexagon II”

Leonardo special issue

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

Brent Collins: Stacked Saddles

Scherk s 2nd minimal surface

Scherk’s 2nd Minimal Surface




Generalization to

higher-order saddles(monkey saddle)

Hyperbolic hexagon by b collins

“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

Closing the Loop




Brent collins prototyping process

Brent Collins’ Prototyping Process

Mockup for the "Saddle Trefoil"

Armature for the "Hyperbolic Heptagon"

Time-consuming ! (1-3 weeks)

Sculpture generator i gui

“Sculpture Generator I”, GUI

A simple scherk collins toroid

A Simple Scherk-Collins Toroid


  • 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

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

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

180 arch half a scherk toroid

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



MonkeySaddles(Radiance 40 hours)

Jane Yen

How to obtain a real sculpture

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

Collins’ Fabrication Process

Wood master patternfor sculpture

Layered laminated main shape

Example: “Vox Solis”

Slices through minimal trefoil

Slices through “Minimal Trefoil”













Profiled slice through the sculpture

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

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 heptoroid

The Finished “Heptoroid”

  • at Fermi Lab Art Gallery (1998).

Sff solid free form fabrication

SFF (Solid Free-form Fabrication)




Fused deposition modeling fdm

Fused Deposition Modeling (FDM)

Zooming into the fdm machine

Zooming into the FDM Machine

Various scherk collins sculptures

Various “Scherk-Collins” Sculptures

Part ii

Part II



Sculpture Families

(Extending a Paradigm)

Family of symmetrical trefoils

Family of Symmetrical Trefoils



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

Close up of some trefoils

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

Higher-order Trefoils (4th order saddles)

W=1 (Warp)

W=2 

Exploring new ideas w 2

Exploring New Ideas: W=2

  • Going around the loop twice ...

… resulting in an interwoven structure.

9 story intertwined double toroid

9-story Intertwined Double Toroid



casting fromwax original made on3D Systems’“Thermojet”

Stepwise expansion of horizon

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

Contact march 21 23 2003


The computer becomesan amplifier / acceleratorfor the creative process.

S quin s minimal saddle trefoil

Séquin’s “Minimal Saddle Trefoil”

  • bronze cast, gold plated

Minimal trefoils cast and finished by steve reinmuth

Minimal Trefoils -- cast and finished by Steve Reinmuth

Steve reinmuth

Steve Reinmuth

Brent collins pax mundi

Brent Collins’ “Pax Mundi”

A new inspiration

Keeping up with brent

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

Part III

The “Least Understood” Step

(Capturing a Paradigm)

Sculptures by naum gabo

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

2-period Gabo Curve

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

4 period gabo curve

4-period Gabo Curve

Same construction as for a 2-period curve

Pax mundi revisited

“Pax Mundi” Revisited

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

Slide ui for pax mundi shapes

SLIDE-UI for “Pax Mundi” Shapes

Viae globi family roads on a sphere

“Viae Globi” Family (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 paradigm

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

Circle Splines on the Sphere

Examples from Jane Yen’s Editor Program

(= another piece of “scaffolding”)

Via globi virtual design

Via Globi -- Virtual Design

Wilmin Martono

Maloja fdm part

“Maloja”(FDM part)

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



  • An even more convoluted alpine pass in Italy.



  • Celebrating American multi-lane highways.



  • A very famous crooked street in San Francisco

  • Note that I switched to a flat ribbon.

Part iv

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

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

Stan Wagon, Macalester College, St. Paul, MN

  • Leader of Team “USA – Minnesota”

Breckenridge 1999

Breckenridge, 1999

Helaman Ferguson: “Invisible Handshake”

Breckenridge 2000

Breckenridge, 2000

Robert Longhurst:

“Rhapsody in White”

2nd Place

Breckenridge 2002

Breckenridge, 2002

Bathsheba Grossman:

“A Twist in Time”

Honorable Mention

“Expressive Impact”

Monkey saddle trefoil

Monkey Saddle Trefoil

from Sculpture Generator I



3D-Print FDM

Name story

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.



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

Construction drawings

Construction Drawings

Top View Side View Axial View

Remove these prisms first!

Day 1

Day 1

Removing lot’s of snow …

Day 1 the monolith

Day 1: The “Monolith”

Cut away prisms …

Day 2 making a torus

Day 2: Making a Torus

Mark center, circles … Bull’s-eye !

Chipping away

Chipping away …

End of day 2

End of Day 2

The Torus

Day 3 am drawing flanges

Day 3, am: Drawing Flanges

Day 3 pm flanges holes

Day 3, pm: Flanges, Holes

Day 4 geometry refinement

Day 4: Geometry Refinement

End of day 4 desired geometry

End of Day 4: Desired Geometry

Day 5 am surface refinement

Day 5, am: Surface Refinement

House cleaning

“House Cleaning”

Whirled white web

“Whirled White Web”

Official team photo

Official Team Photo

Part v

Part V


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


The starting point

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

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

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

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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