Art & Science UCB DeCal, September 17, 2013 Carlo H. Séquin University of California, Berkeley

SCIENCE ART MATH DESIGN

What came first: Art or Mathematics ? u Question posed Nov. 16, 2006 by Dr. Ivan Sutherland “father” of computer graphics (SKETCHPAD, 1963).

Early “Free-Form” Art Cave paintings, LascauxVenus von Willendorf

Regular, Geometric Art u Early art: Patterns on bones, pots, weavings... u Mathematics (geometry) to help make things fit:

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... between Art and Design ?

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

Unfinished Construction Site ?

Clearly Something Special... Art? or Design?

Art or Wallpaper ?

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

Another Mysterious Object u Propeller for a submarin ? u Grinder head for tunnel boring ? u Galactic force concentrator ?

My Background: Geometry ! u Descriptive Geometry – love since high school

Descriptive Geometry

40 Years of Geometry and Design CCD TV Camera Soda Hall RISC 1 Computer Chip Octa-Gear (Cyberbuild)

More Recent Creations

Aurora Sculptures Inspired by the curtain- or ribbon-like Northern Lights

Torus-Knot_5,3 Inspired by a well defined type of mathematical knot Torus-Knot_3,5

A Special Result

The Process: ( For Scherk-Collins Toroids ) Inspirational Model Generative Paradigm Computer Program Many New Models Insight, Analysis Math, Geometry Selection, Design

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

Brent Collins: Hyperbolic Hexagon

Scherk’s 2nd Minimal Surface 2 planes the central core 4 planes bi-ped saddles 4-way saddles = “Scherk tower”

Scherk’s 2nd Minimal Surface Normal “biped” saddles Generalization to higher-order saddles (monkey saddle) “Scherk Tower”

V-art (1999) Virtual Glass Scherk Tower with Monkey Saddles (Radiance 40 hours) Jane Yen

Closing the Loop straight or twisted “Scherk Tower”“Scherk-Collins Toroids”

Sculpture Generator 1, GUI

Shapes from Sculpture Generator 1

Inauguration Sutardja Dai Hall 2/27/09

The Finished Heptoroid u at Fermi Lab Art Gallery (1998).

2003: “Whirled White Web”

12:40 pm -- 42° F

12:41 pm -- 42° F

“WWW” Wins Silver Medal

Brent Collins and David Lynn

Sculpture Generator #2

Tentative Assembly of Three Units

Yet Another Medium: Stone “The Three Pillars of Engineering” Math – Materials – Physics(Science) Sponsored by Paul Suciu (EECS alum)

Spring, 2012

Inauguration Sutardja Dai Hall 2/27/09

The Viae Globi Series u Another example how one special piece of art led 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’ Pax Mundi 1997: wood, 30”diam. 2006: Commission from H&R Block, Kansas City to make a 70”diameter version in bronze. My task: Define the master geometry. CAD tools play important role!

How to Model Pax Mundi... u Already addressed that question in 1998: u Pax Mundi could not be done with Sculpture Generator I u Needed a more general program ! u Used the Berkeley SLIDE environment. u First: Needed to find the basic paradigm   

Sculptures 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” u Approximation with quartic B-spline with 8 control points per period, but only 3 DOF are used (symmetry!).

4-period “Gabo Curve” Same construction as for as for 2-period curve

Pax Mundi Revisited u Can be seen as: Amplitude modulated, 4-period Gabo curve

SLIDE-GUI for “Pax Mundi” Shapes Good combination of interactive 3D graphics and parameterizable procedural constructs.

2-period Gabo Sculpture Tennis ball – or baseball – seam used as sweep curve.

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

Via Globi 5 (Virtual Wood) Wilmin Martono

Modularity of Gabo Sweep Generator u Sweep Curve Generator: l Gabo Curves as B-splines u Cross Section Fine Tuner: l Paramererized shapes u Sweep / Twist Controller

Sweep / Twist Control u How do we orient, move, scale, morph... the cross section along the sweep path ? Natural orientation with Frenet frame Torsion Minimization: Azimuth: tangential / normal 900° of twist added.

Target Geometry (2007) Constraints: Bronze, 70” diameter Less than 1500 pounds Less than $50’000 Maintain beauty, strength Minimize master geometry

Emulation; Define Master Pattern u Use 4 copies. u Master to make a mold from. Alignment tab

Joe Valasek’s CNC Milling Machine u Styrofoam milling machine

Machined Master Pattern #2

(Cut) Master  Silicone Rubber Mold

Mold  Several (4) Wax Copies

Spruing the Wax Parts for Casting

Ceramic Slurry Shell Around Wax Part

Taking the Shell out of the Kiln

Shell Ready for Casting

The Pour

Casting with Liquid Bronze

Freeing the Bronze Cast

Assembling the Segments

The “Growing” Ribbon

Assembly Completed Assembly Completed

Front Door of the... H&R Block Building

Steve Reinmuth, Bronze Studio, Eugene OR u

Team effort: Brent Collins, Steve Reinmuth, Carlo Séquin

The Process: Example: Pax Mundi Wood Pax Mundi Sweep curve on a sphere Via Globi framework In SLIDE Bronze Pax Mundi Inspirational Model Generative Paradigm Computer Program Many New Models Insight, Analysis Math, Geometry Selection, Design

Extension: Free-form Curve on a Sphere Spherical Spline Path Editor (Jane Yen) Smooth interpolating curve through sparse data points

Many Different Viae Globi Models

Music of the Spheres (Brent Collins) Paradigm Extension: Sweep Path is no longer confined to a sphere!

Partitioning; Joint Design 18 pieces: fit in kiln! 1/3 = unique geometry Alignment stubs

Some Segments Will Be Cast Hollow This needs a double-walled tube mold!

Some of the Hollow Metal Parts

Assembly of Music of the Spheres

Installation at MWSU, Feb Steve Reinmuth Brent Collins

Illuminated Music of the Spheres Photo by Phillip Geller

Conclusions u Knotted and twisted structures play an important role in many areas of physics and the life sciences. u They also make fascinating art-objects...

Is It Math ? Is It Art ? u it is: “KNOT-ART”

QUESTIONS ? ?