Collections:
John Neuberger, Robert Renka, Fan Chung and Ron Graham
Exhibitions:
National Science Foundation, January - August 2001;
Joint Meetings of the AMS, MAA, SIAM, Baltimore, January 2002;
ICIAM July 2003 Sydney, New South Wales, Australia at the
Harbour Convention Centre;
Joint Meetings of the AMS, MAA, SIAM, Phoenix, January 2004
Provenance:
Commissioned by Professor John W. Neuberger, Mathematics,
University of North Texas. John and his colleague Robert Renka in
collaboration with Michel L. Lapidus and especially Cheryl A. Griffith,
numerically computed the first forty
eigenfunctions on the Helge Koch fractal snowflake curve. The 13th has
seven bumps and sixfold symmetry.
Special engraving:
13th eigenfunction of Laplace-Dirichlet with a fractal snowflake
boundary ∂D,
13th eigenvalue ≈ F\>#,
∂F²/∂u² + ∂F²/∂v² = 0,
F = 0 on ∂D
Dimensions:
Weight:
Materials:
Solid silicon bronze, polished
Price:
Copyright:
Imagine a drum made by stretching a membrane over a snowflake
fractal closed curve drumhead. What would it sound like? What would be its
fundamental frequencies or normal modes? This bronze image is a physical
approximation to the mathematical reality of the 13th eigenvalue, which
mathematically happens to occur near F
\>#.
Cf., Ivars Peterson, "Beating a Fractal Drum",SCIENCE NEWS,
Volume 146, Number 12, September 17, 1994, pages 184-185, cover
" Spiderflake Drum " reporting on the Neuberger-Renka
computation for the Dirichlet boundary condition.
This was a very non-trivial numerical computation.
Lately, I believe some of these computations have been redone by other
methods by student(s) of Nick Trevethen, Cambridge, UK. Time will tell.
Photo credit, Sunforge Studios
