A hyperhelix of order N is defined to be a self-similar object consisting o
f a thin elastic rod wound into a helix, which is itself wound into a large
r helix, until this process has been repeated N times. Wave propagation on
such a structure can be discussed in a hierarchical manner, ultimately in t
erms of the wavenumber k defining propagation on the elementary rod. It is
found that the dispersion curve expressing the wave frequency omega as a fu
nction of the elementary wavenumber k on the rod making up the initial heli
x is also a fractal object, with all the macroscopically observable wave ph
enomena for a hyperhelix of arbitrarily large order being compressed into a
small wavenumber range of width about 2R(2)(-1)alpha centred on the value
k = R-1(-1), where R-1 is the radius, ct is the helical pitch angle of the
smallest helix in the progression, and R-2 is the radius of the next-larger
helix.