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Leonardo Meeting, SETI Institute, Feb. 10, 2010 Naughty Knotty Sculptures Carlo H. Séquin U.C....
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Transcript of Leonardo Meeting, SETI Institute, Feb. 10, 2010 Naughty Knotty Sculptures Carlo H. Séquin U.C....
Leonardo Meeting, SETI Institute, Feb. 10, 2010Leonardo Meeting, SETI Institute, Feb. 10, 2010
NaughtyKnotty Sculptures
Carlo H. Séquin
U.C. Berkeley
But This: But This: Sculptures Made from Knots Sculptures Made from Knots
Knots as constructive sculptural building blocks.
Technical Designs …Technical Designs …
CCD Camera, Bell Labs, 1973 Soda Hall, Berkeley, 1994
RISC chip, Berkeley, 1981 “Octa-Gear”, Berkeley, 2000
Since 1994: Aesthetic Designs …Since 1994: Aesthetic Designs …
What is the role of the computer in:
aesthetic optimization,
the creative process ?
Rapid Prototyping Model of the 24-CellRapid Prototyping Model of the 24-Cell
Noticethe 3-fold
permutationof colors
Made on the Z-corp machine.
Tetra Trefoil TanglesTetra Trefoil Tangles
Simple linking (1) -- Complex linking (2)
{over-over-under-under} {over-under-over-under}
Platonic Trefoil TanglesPlatonic Trefoil Tangles
Take a Platonic polyhedron made from triangles,
Add a trefoil knot on every face,
Link with neighboring knots across shared edges.
Icosahedral Icosahedral Trefoil Trefoil TangleTangle(type 3)(type 3)
Doubly linked with each neighbor
Realization by ProMetal (Ex One Co.)Realization by ProMetal (Ex One Co.)
Metal sintering and infiltration process
““The Beauty of Knots”The Beauty of Knots”
Undergraduate research group in 2009
More recently, I have been looking for sculptureswhere the whole piece is just a single knot.
Make aesthetically pleasing artifacts!
PART BPART BComputer-Generated KnotsComputer-Generated Knots
I. Bottom-up knot construction
II. Fusing simple knots together
III. Top-down mesh infilling
IV. Longitudinal knot splitting
Generate knots & increase their complexity in a structured, procedural way.
Explore several different methods…
““Hilbert” Curve in 3D (1999)Hilbert” Curve in 3D (1999)
Start with Hamiltonian path on cube edges and recurse ...
Replaces an “elbow”
Jane Yen: “Jane Yen: “Hilbert Radiator PipeHilbert Radiator Pipe” ” (2000)(2000)
Flaws( from a sculptor’s . point of view ):
4 coplanar segments
Not a closed loop
Broken symmetry
A Knot Theorist’s ViewA Knot Theorist’s View
It is still just the un-knot !
Thus our construction element should use a “more knotted thing”:
e.g. an overhand knot:
A Knot Theorist’s ViewA Knot Theorist’s View
This is just a compound-knot !
It does not really lead to a complex knot !
Thus our assembly step should cause a more serious entanglement:
adjacent knots should entangle one another, or
crossing strands should be knotted together . . .
OutlineOutline
I. Bottom-up knot construction
II. Fusing simple knots together
III. Top-down mesh infilling
IV. Longitudinal knot splitting
From Paintings to SculpturesFrom Paintings to Sculptures
Do something like this in 3D !
Perhaps using two knotted strands(like your shoe laces).
A “Knotty” “3D” Recursion StepA “Knotty” “3D” Recursion Step
Use the Granny knot as a replacement element where two strands cross ...
One More Recursion StepOne More Recursion Step
Now use eight of these composite elements;
connect;
beautify. Too much
com
plexity
!
Too much
com
plexity
!
OutlineOutline
I. Bottom-up knot construction
II. Fusing simple knots together
III. Top-down mesh infilling
IV. Longitudinal knot splitting
Recursive Figure-8 Knot Recursive Figure-8 Knot (4 crossings)(4 crossings)
Recursion stepMark crossings over/under to form alternating knot
Result after 2 more recursion steps
Recursive Figure-8 KnotRecursive Figure-8 Knot
Scale the stroke-width proportional to recursive reduction
2.5D Recursive (Fractal) Knot2.5D Recursive (Fractal) Knot
Robert Fathauer: “Recursive Trefoil Knot”
Trefoil Recursion3 views step
From 2D Drawings to 3D SculptureFrom 2D Drawings to 3D Sculpture
Too flat ! Switch plane orientations
OutlineOutline
I. Bottom-up knot construction
II. Fusing simple knots together
III. Top-down mesh infilling
IV. Longitudinal knot splitting
Splitting Moebius BandsSplitting Moebius Bands
Litho by FDM-model FDM-modelM.C.Escher thin, colored thick