Art & Science

UCB DeCal, September 17, 2013UCB DeCal, September 17, 2013

Carlo H. Séquin

University of California, Berkeley

SCIENCESCIENCEARTART

MATHMATH

DESIGNDESIGN

What came first: Art or Mathematics ?What came first: Art or Mathematics ?

Question posed Nov. 16, 2006 by Dr. Ivan Sutherland“father” of computer graphics (SKETCHPAD, 1963).

Early “Free-Form” ArtEarly “Free-Form” Art

Cave paintings, Lascaux Venus von Willendorf

Regular, Geometric ArtRegular, Geometric Art

Early art: Patterns on bones, pots, weavings...

Mathematics (geometry) to help make things fit:

Another Question:Another Question:

What came first: Art or Science?

What is Art ? -- What do artists do ?

What is Science ? -- What do scientists do ?

What is the Difference . . .What is the Difference . . .

between between ArtArt and and DesignDesign ? ?

Art? -- or Design? -- or What?Art? -- or Design? -- or What?

Art? -- or Design? -- or What?Art? -- or Design? -- or What?

Unfinished Construction Site ?Unfinished Construction Site ?

Clearly Something Special . . .Clearly Something Special . . .

Art? or Design?

Art or Wallpaper ?Art or Wallpaper ?

Art? -- or Design? -- or What?Art? -- or Design? -- or What?

Another Mysterious ObjectAnother Mysterious Object

Propeller for a submarin ?

Grinder head for tunnel boring ?

Galactic force concentrator ?

My Background: Geometry ! My Background: Geometry !

Descriptive Geometry – love since high school

Descriptive GeometryDescriptive Geometry

40 Years of Geometry and Design40 Years of Geometry and Design

CCD TV Camera Soda Hall

RISC 1 Computer Chip Octa-Gear (Cyberbuild)

More Recent CreationsMore Recent Creations

Aurora SculpturesAurora Sculptures

Inspired by the curtain- or ribbon-like Northern Lights

Torus-Knot_5,3Torus-Knot_5,3

Inspired by a well defined type of mathematical knot

Torus-Knot_3,5

A Special ResultA Special Result

The Process: (The Process: (For Scherk-Collins ToroidsFor Scherk-Collins Toroids))

InspirationalModel

GenerativeParadigm

ComputerProgram

Many NewModels

Insight,Analysis

Math,Geometry

Selection,Design

Scherk-Collins ToroidsScherk-Collins Toroids

Collaboration with sculptor Brent Collins: “Hyperbolic Hexagon” 1994 “Hyperbolic Hexagon II”, 1996 “Heptoroid”, 1998

Brent Collins: Brent Collins: Hyperbolic HexagonHyperbolic Hexagon

ScherkScherk’’s 2nd Minimal Surfaces 2nd Minimal Surface

2 planes the central core 4 planesbi-ped saddles 4-way saddles

= “Scherk tower”

ScherkScherk’’s 2nd Minimal Surfaces 2nd Minimal Surface

Normal“biped”saddles

Generalization to higher-order saddles(monkey saddle)“Scherk Tower”

V-artV-art(1999)(1999)

VirtualGlassScherkTowerwithMonkeySaddles

(Radiance 40 hours)

Jane Yen

Closing the LoopClosing the Loop

straight

or

twisted

“Scherk Tower” “Scherk-Collins Toroids”

Sculpture Generator 1Sculpture Generator 1, GUI , GUI

Shapes from Shapes from Sculpture Generator 1Sculpture Generator 1

Inauguration Sutardja Dai Hall 2/27/09Inauguration Sutardja Dai Hall 2/27/09

The Finished The Finished HeptoroidHeptoroid

at Fermi Lab Art Gallery (1998).

2003: 2003: ““Whirled White WebWhirled White Web””

12:40 pm -- 4212:40 pm -- 42° F° F

12:41 pm -- 4212:41 pm -- 42° F° F

““WWWWWW”” Wins Silver Medal Wins Silver Medal

Brent Collins and David LynnBrent Collins and David Lynn

Sculpture Generator #2Sculpture Generator #2

Tentative Assembly of Three UnitsTentative Assembly of Three Units

Yet Another Medium: Yet Another Medium: StoneStone

“The Three Pillars of Engineering”Math – Materials – Physics(Science)

Sponsored by Paul Suciu (EECS alum)

Spring, 2012Spring, 2012

Inauguration Sutardja Dai Hall 2/27/09Inauguration Sutardja Dai Hall 2/27/09

The The Viae Globi Viae Globi SeriesSeries

Another example how one special piece of artled to a computer program, which then allowed me to make a whole series of sculpture designs that all seem to belong to the same family.

(Roads on a Sphere)

Brent Collins’ Brent Collins’ Pax MundiPax Mundi

1997: wood, 30”diam.1997: wood, 30”diam.

2006: Commission from H&R Block, Kansas Cityto make a 70”diameter

version in bronze.

My task: Define the master geometry.

CAD tools play important role!

How to Model How to Model Pax MundiPax Mundi ... ...

Already addressed that question in 1998:

Pax Mundi could not be done with Sculpture Generator I

Needed a more general program !

Used the Berkeley SLIDE environment.

First: Needed to find the basic paradigm

Sculptures by Naum GaboSculptures by Naum Gabo

Pathway on a sphere:

Edge of surface is like seam of tennis- or base-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 (symmetry!).

4-period “Gabo Curve”4-period “Gabo Curve”

Same construction as for as for 2-period curve

Pax MundiPax Mundi Revisited Revisited

Can be seen as:

Amplitude modulated, 4-period Gabo curve

SLIDE-GUI for “SLIDE-GUI for “Pax MundiPax Mundi” Shapes” ShapesGood combination of interactive 3D graphicsand parameterizable procedural constructs.

2-period Gabo Sculpture2-period Gabo Sculpture

Tennis ball – or baseball –

seam used as

sweep curve.

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

2 3 4 5 periods

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

Wilmin Martono

Modularity of Modularity of Gabo Sweep GeneratorGabo Sweep Generator

Sweep Curve Generator:

Gabo Curves as B-splines

Cross Section Fine Tuner:

Paramererized shapes

Sweep / Twist Controller

Sweep / Twist ControlSweep / Twist Control

How do we orient, move, scale, morph ...the cross section along the sweep path ?

Natural orientationwith Frenet frame

Torsion Minimization:Azimuth: tangential / normal

900° of twistadded.

Target GeometryTarget Geometry(2007)(2007)

Constraints:• Bronze, 70” diameter• Less than 1500 pounds• Less than $50’000• Maintain beauty, strength• Minimize master geometry

Emulation; Define Master PatternEmulation; Define Master Pattern

Use 4 copies.

Master to make a mold from.

Alignment tab

Joe ValasekJoe Valasek’’s CNC Milling Machines CNC Milling Machine

Styrofoam milling machine

Machined Master Pattern #2Machined Master Pattern #2

(Cut) Master (Cut) Master Silicone Rubber MoldSilicone Rubber Mold

MoldMold Several (4) Wax Copies Several (4) Wax Copies

SpruingSpruing the the Wax PartsWax Parts for Casting for Casting

Ceramic Slurry ShellCeramic Slurry Shell Around Wax Part Around Wax Part

Taking the Taking the ShellShell out of the out of the KilnKiln

ShellShell Ready Ready for Castingfor Casting

The The PourPour

Casting with Casting with Liquid BronzeLiquid Bronze

Freeing the Freeing the Bronze CastBronze Cast

Assembling the SegmentsAssembling the Segments

The The ““GrowingGrowing”” Ribbon Ribbon

Assembly CompletedAssembly Completed

Front Door of the ...Front Door of the ...

H&R Block Building

Steve ReinmuthSteve Reinmuth, , Bronze Studio, Eugene ORBronze Studio, Eugene OR

http://www.reinmuth.com/

Team effort: Brent Collins, Steve Reinmuth, Carlo Séquin

The Process: Example: The Process: Example: Pax MundiPax Mundi

WoodPax Mundi

Sweep curve on a

sphere

ViaGlobi

frameworkIn SLIDE

Bronze Pax Mundi

InspirationalModel

GenerativeParadigm

ComputerProgram

Many NewModels

Insight,Analysis

Math,Geometry

Selection,Design

Extension:Extension: Free-form Curve on a Sphere Free-form Curve on a Sphere

Spherical Spline Path Editor (Jane Yen)

Smooth interpolating curve through sparse data points

Many Different Many Different Viae GlobiViae Globi ModelsModels

Music of the Spheres (Brent Collins)

Paradigm Extension:Paradigm Extension: Sweep Path Sweep Path is no longer confined to a sphere!is no longer confined to a sphere!

Partitioning; Joint DesignPartitioning; Joint Design

18 pieces:fit in kiln!

1/3 = uniquegeometry

Alignment stubsAlignment stubs

Some Segments Will Be Cast HollowSome Segments Will Be Cast Hollow

This needs a double-walled

tube mold!

Some of the Hollow Metal PartsSome of the Hollow Metal Parts

Assembly of Assembly of Music of the SpheresMusic of the Spheres

Installation at MWSU, Feb. 2013Installation at MWSU, Feb. 2013

Steve Reinmuth Brent Collins

Illuminated Illuminated Music of the SpheresMusic of the Spheres

Photo by Phillip Geller

ConclusionsConclusions

Knotted and twisted structures play an important role in many areas of physics and the life sciences.

They also make fascinating art-objects . . .

Is It Math ?Is It Math ?Is It Art ?Is It Art ?

it is:

“KNOT-ART”

QUESTIONS ?QUESTIONS ?

?