MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

94 Applications
(a)
Figure 3.23: Loudspeaker Array: (a) Icosahedral Speaker. (b) Equilateral
Triangle Array. [13]
Application 23 (Icosahedral Speaker). The research team at The Center
for New Music and Audio Technologies (CNMAT) of UC-Berkeley, in collaboration
with Meyer Sound of Berkeley, California, has created a compact 120channel
approximately spherical loudspeaker for experiments with synthesis of
acoustic signals with real-time programmable directional properties.
These directional patterns can reproduce the complete radiative signature
of natural instruments or explore new ideas in spatial audio synthesis. A
special hybrid geometry is used that combines the maximal symmetry of a
twenty-triangular-faceted icosahedron (Figure 3.23(a)) with the compact planar
packing of six circles on an equilateral triangle (Figure 3.23(b) shows the
resulting “billiard ball packing”.) [13].
Application 24 (Superconducting Sierpinski Gasket). In 1986, Gordon
et al. [147] reported on their experimental investigations of the properties of a
superconducting Sierpinski gasket (SG) network in a magnetic field.
Because of their dilational symmetry, statistical mechanical and transport
problems are exactly solvable on these fractals. Moreover, study of the SG
network is inherently interesting because of its lack of translational invariance
and its anomalous (fractal) dimensionalities. The experimental gaskets (Figure
3.24) were of tenth order with elementary triangles of area 1.38 µm 2 and
produced excellent quantitative agreement with theoretical predictions.
(b)