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

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

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)

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:

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

Honda (Element) “Purpose” Director: Roman Coppola

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

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

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

Torus-Costa’s Minimal Surface Metamorphosis

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

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

Sachiko Kodama, Tokyo Protrude, Flow 2001

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

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

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

Stewart Dickson