DIMENSION MEASUREMENT ON HIGH-DIMENSIONAL SYSTEMS

Using experimental data from a variety of laboratory electrical systems the upper limits on dimension measurement are examined, and it is shown that contrary to standard scaling estimates it can be possible to reliably measure correlation dimensions larger than 10. The practical implications of the constraints on such a measurement are examined, including the role of statistical errors, geometrical artifacts, dimension algorithm, metric choice, and the process power spectrum. These ideas are applied to electrical 1/f noise from both macroscopic and microscopic sources to show that it cannot be explained by a deterministic model with fewer than roughly 20 degrees of freedom.