  We use a bath of chaotic surface waves in water to mechanically and
macroscopically mimic the thermal behavior of a short articulated chain with
only nearest-neighbor interactions. The chaotic waves provide isotropic and
random agitation to which a temperature can be ascribed, allowing the chain to
passively explore its degrees of freedom in analogy to thermal motion. We track
the chain in real time and infer end-to-end potentials using Boltzmann
statistics. We extrapolate our results, by using Monte Carlo simulations of
self-avoiding polymers, to lengths not accessible in our system. In the long
chain limit we demonstrate universal scaling of the statistical parameters of
all chains in agreement with well-known predictions for self-avoiding walks.
However, we find that the behavior of chains below a characteristic length
scale is fundamentally different. We find that short chains have much greater
compressional stiffness than would be expected. However, chains rapidly soften
as length increases to meet with expected scalings.
