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

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

3. 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 http://emsh.calarts.edu/~mathart/Zoetrope2/Zoetrope2_prop.html Calabi-Yau Manifold (with Andrew Hanson)

4. 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:

8. http://emsh.calarts.edu/~mathart/portfolio/CG_Bronze/CG_bronze.html

11. 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

12. http://www.swaystudio.com Honda (Element) “Purpose” Director: Roman Coppola

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

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

15. http://emsh.calarts.edu/~mathart/IS99_Talk/IS99_Contents.html

16. http://www.tinialloy.com/ TiNi alloy Company’s Thin Film Shape Memory Alloy Proportionally Controlled Microvalve

17. http://emsh.calarts.edu/~mathart/IS99_Talk/IS99_Contents.html

18. Torus-Costa’s Minimal Surface Metamorphosis http://emsh.calarts.edu/~mathart/Zoetrope.html

19. 3-D Zoetrope of the Torus-Costa’s Surface Metamorphosis http://emsh.calarts.edu/~mathart/Zoetrope.html

31. 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

36. Sachiko Kodama, Tokyo Protrude, Flow 2001

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

38. http://llk.media.mit.edu/projects/cricket/

39. http://www.lego.com/dacta/products/productsbyproductline.asp

45. http://emsh.calarts.edu/~mathart/Cell_Auto/CellAutoSculpt_prop_Contents.html

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

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

58. Stewart Dickson http://us.imdb.com/Name?Stewart+Dickson http://emsh.calarts.edu/~mathart http://www.cs.utk.edu/~dickson http://www.csm.ornl.gov/~dickson DicksonSP@ornl.gov Mathart@emsh.calarts.edu