  In this paper we examine the concept of complexity as it applies to
generative and evolutionary 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 evolutionary 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 generative 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 then assess
the value of complexity measures for the audience by undertaking a large-scale
survey on the perception of complexity and aesthetics. 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.
