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An Apparatus for Performing Real-time, Interactive Sculpture Stewart Dickson, Visualization Researcher Computer Science and Mathematics Division

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“ What I hear I forget, What I see I remember, What I touch I understand.” -Confucius ( b. 09/28/0555 BC)

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u1[a_,b_] :=.5 (E(a + I*b) + E(- a - I*b)) u2[a_,b_] :=.5 (E(a + I*b) - E(- a - I*b)) z1k[a_,b_,n_,k_] := E(k*2*Pi*I/n)*u1[a,b](2.0/n) z2k[a_,b_,n_,k_] := E(k*2*Pi*I/n)*u2[a,b](2.0/n) {x, y, z} -> { Re[z1k[a,b,n,k1]], Re[z2k[a,b,n,k2]], Cos[alpha]*Im[z1k[a,b,n,k1]] + Sin[alpha]*Im[z2k[a,b,n,k2]]} a: (-1.0,1.0); b:(0, Pi/2); k2: (0, n - 1) k1: (0, n - 1) Tactile Mathematics is An Immediate Experience Calabi-Yau Manifold (with Andrew Hanson)

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r1 = 1.0 r2 = 3.0 Bx [u_, v_] := (r2 + r1 * Cos[u/2.0]) * Cos[u/3.0] By [u_, v_] := (r2 + r1 * Cos[u/2.0]) * Sin[u/3.0] Bz [u_, v_] := r1 * Sin[u/2.0] x [u_, v_] := N[Bx [u, v]] + r1 * Cos[u/3.0] * Cos[v - Pi] y [u_, v_] := N[By [u, v]] + r1 * Sin[u/3.0] * Cos[v - Pi] z [u_, v_] := N[Bz [u, v]] + r1 * Sin[v - Pi] Trefoil Torus-Knot:

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h tt p :/ / w w w. e ri c h a r s h b a r g e r. o r g /l e g o More Layer Manufacturing

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Honda (Element) “Purpose” Director: Roman Coppola

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Daniel Rozin, New York University (NYU) Shiny Balls Mirror, 2003

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Daniel Rozin, New York University (NYU) Shiny Balls Mirror, 2003

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TiNi alloy Company’s Thin Film Shape Memory Alloy Proportionally Controlled Microvalve

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Torus-Costa’s Minimal Surface Metamorphosis

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3-D Zoetrope of the Torus-Costa’s Surface Metamorphosis

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u1[a_,b_] :=.5 (E(a + I*b) + E(- a - I*b)) u2[a_,b_] :=.5 (E(a + I*b) - E(- a - I*b)) z1k[a_,b_,n_,k_] := E(k*2*Pi*I/n)*u1[a,b](2.0/n) z2k[a_,b_,n_,k_] := E(k*2*Pi*I/n)*u2[a,b](2.0/n) {x, y, z} -> { Re[z1k[a,b,n,k1]], Re[z2k[a,b,n,k2]], Cos[alpha]*Im[z1k[a,b,n,k1]] + Sin[alpha]*Im[z2k[a,b,n,k2]]} a: (-1.0,1.0); b:(0, Pi/2); k2: (0, n - 1) k1: (0, n - 1) Calabi-Yau Manifold/Fermat Surface As a Superquadric Surface Parameterized in CP4

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Sachiko Kodama, Tokyo Protrude, Flow 2001

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‘Pseudopod’ from “The Abyss” © 1989 Twentieth Century Fox

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Stephen Wolfram 2-D Cellular Automaton -- Rule 924 “A New Kind of Science”

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‘Pseudopod’ from “The Abyss” © 1989 Twentieth Century Fox

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Stewart Dickson

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