  In this paper we examine the concept of complexity as it applies to
generative art and design. Complexity has many different, discipline specific
definitions, such as complexity in physical systems (entropy), algorithmic
measures of information complexity and the field of "complex systems". We apply
a series of different complexity measures to three different generative art
datasets and look at the correlations between complexity and individual
aesthetic judgement by the artist (in the case of two datasets) or the
physically measured complexity of 3D forms. Our results show that the degree of
correlation is different for each set and measure, indicating that there is no
overall "better" measure. However, specific measures do perform well on
individual datasets, indicating that careful choice can increase the value of
using such measures. We conclude by discussing the value of direct measures in
generative and evolutionary art, reinforcing recent findings from neuroimaging
and psychology which suggest human aesthetic judgement is informed by many
extrinsic factors beyond the measurable properties of the object being judged.
