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of the “play within a play.” Claudius, who wishes to hide the murder of
Hamlet's father, looks fi rst to deception, is plagued by moral thought, and
succumbs to impulse in the poisoning of swords. Regardless of the charac-
ters involved, the audience typically knows something that the characters
don't. In most scenes, a plan made by a central character is thwarted sud-
denly by a reversal near the end of the scene. Patterns within patterns lay
out these elements in different combinations. What we have, then, is a play
with nested parts that rework its major themes in a particular manner in-
volving reversal for the characters. Each of these scenes can be said to be
self-similar at scale, even though the pattern of the scene or act may involve
a recombination of forces.
Science tells us that such self-similarity of dimensions or parts of a thing
in relation to the whole is pervasively true of natural phenomena. Richard
Voss and John Clarke (1976) identifi ed the temporal manifestation of fractals
in the mathematical expression of 1 over
f
noise, commonly called “pink
noise,” which produces the pleasure of the fractal phenomenon on the audi-
tory level. Mandelbrot and Frame (2002) tell the story of Voss' discoveries:
As a graduate student at Berkeley, Richard Voss was studying this prob-
lem, using signal-processing equipment and computers to produce the
power spectrum of the signal from a semiconductor sample. When one
sample had burned out and another was being prepared, Voss plugged
his signal-analyzing equipment into a radio and computed the power
spectrum. Amazingly, a 1/
f
spectrum appeared. Voss changed radio sta-
tions and repeated the experiment—another 1/
f
distribution. Classical,
jazz, blues, and rock all exhibited 1/
f
distributions. Even radio news and
talk shows gave (approximate) 1/
f
distributions.
Mandelbrot and Frame have documented
1/
f
noise in Western music
as well as African, Japanese, Indian, and Russian and through a range of
times, from the Medieval period through the Beatles. They conclude:
Voss uses these observations eloquently to bring closure to one of the
classical Greek theories of art. The Greeks believed art imitates nature,
and how this happens is relatively clear for painting, sculpture, and
drama. Music, though, was a puzzle. Except for rare phenomena such as
aeolian harps, few processes in Nature seem musical. Voss uses the ubiq-
uity of 1/
f
noise to assert [that] music mimics
the way the world changes
with time
.
