  Our goal in this paper is to develop an effective estimator of fractal
dimension. We survey existing ideas in dimension estimation, with a focus on
the currently popular method of Grassberger and Procaccia for the estimation of
correlation dimension. There are two major difficulties in estimation based on
this method. The first is the insensitivity of correlation dimension itself to
differences in dimensionality over data, which we term "dimension blindness".
The second comes from the reliance of the method on the inference of limiting
behavior from finite data.
  We propose pointwise dimension as an object for estimation in response to the
dimension blindness of correlation dimension. Pointwise dimension is a local
quantity, and the distribution of pointwise dimensions over the data contains
the information to which correlation dimension is blind. We use a "limit-free"
description of pointwise dimension to develop a new estimator. We conclude by
discussing potential applications of our estimator as well as some challenges
it raises.
