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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



Scherk s 2nd minimal surface
Scherk’s 2nd Minimal Surface

Normal

“biped”

saddles

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

straight

or

twisted


Brent collins prototyping process
Brent Collins’ Prototyping Process

Mockup for the "Saddle Trefoil"

Armature for the "Hyperbolic Heptagon"

Time-consuming ! (1-3 weeks)



A simple scherk collins toroid
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
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
V-art

VirtualGlassScherkTowerwith

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”

50%

30%

23%

10%

45%

27%

20%

5%

35%

25%

15%

2%


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)

Monkey-

Saddle

Cinquefoil





Part ii
Part II

Developing

Parameterized

Sculpture Families

(Extending a Paradigm)


Family of symmetrical trefoils
Family of Symmetrical Trefoils

W=2

W=1

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

Bronze

investment

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


Note:

The computer becomesan amplifier / acceleratorfor the creative process.





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



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”)



Maloja fdm part
“Maloja”(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 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, 2003Macalester College, St. Paul, MN

  • Leader of Team “USA – Minnesota”


Breckenridge 1999
Breckenridge, 1999 2003

Helaman Ferguson: “Invisible Handshake”


Breckenridge 2000
Breckenridge, 2000 2003

Robert Longhurst:

“Rhapsody in White”

2nd Place


Breckenridge 2002
Breckenridge, 2002 2003

Bathsheba Grossman:

“A Twist in Time”

Honorable Mention

“Expressive Impact”


Monkey saddle trefoil
Monkey Saddle Trefoil 2003

from Sculpture Generator I


Maquettes
Maquettes 2003

3D-Print FDM


Name story
Name, Story 2003

  • “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 ! 2003

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


Construction drawings
Construction Drawings 2003

Top View Side View Axial View

Remove these prisms first!


Day 1
Day 1 2003

Removing lot’s of snow …


Day 1 the monolith
Day 1: The “Monolith” 2003

Cut away prisms …


Day 2 making a torus
Day 2: Making a Torus 2003

Mark center, circles … Bull’s-eye !



End of day 2
End of Day 2 2003

The Torus










Part v
Part V 2003

DISCUSSION:

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

?


The starting point
The Starting Point 2003

  • 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 2003

  • 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 2003

  • 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 ? 2003

  • 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
QUESTIONS ? 2003DISCUSSION ?


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