The Enigma of Complexity

Abstract

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.

Quality-diversity for aesthetic evolution

“…However, the broad principles we have applied make this easy to test. Prior research has shown that while there exists reasonable computable proxies for specific aesthetic preferences [25], the specific measure varies between system and individual, requiring the kind of correlation evaluation we performed in Section 4.1. This requires significant human time, as the individual artist must manually rank or compare a sufficient number of random phenotypes to determine the best correlation with a variety of possible computable measures.…”

“…However, defining some measure of quality is crucial in the context of generative evolutionary art, as it is the 'rein control' [6,12] the artist needs to steer the generative process towards the results they are looking for. Previous work has shown that computable measures are far better at capturing an individual artist's perception of aesthetics in a specific system over collective general perceptions of quality or aesthetic value [25]. Relatively simple measures, such as image complexity [19,20] or information content [29] have been used as fitness measures, for example.…”

“…Human Fitness Evaluation Building on our previous results [25], for this work we wanted to capture the artist's aesthetic preferences for the generative system in a formalised fitness measure. To do this we first generated a number of random phenotypes and asked the artist to evaluate their aesthetic quality using two different methods: direct numerical score and pairwise comparison ranking.…”

“…The same dataset of images were also evaluated using the image feature metrics described in [25]) and statistical measures of image intensity (mean, variance, centroid). The measures tested included image entropy and energy, morphological Euler number, algorithmic and structural complexity, fractal dimensional and fractal aesthetic measures (see [25] for details on each measure). These measures were calculated for each image and then compared to the artist-assigned rankings.…”

“…To determine quality we first generate a random sample of phenotypes and ask the artist to evaluate their aesthetic quality manually, using this evaluation to derive a measure of quality specific to the artist and the system. Based on previous studies, which have suggested image metrics can serve as a good proxy for personal aesthetics [25], we analyse the aesthetically ranked phenotypes, computing various measures of complexity and image morphology, looking for high correlations between these measures and the artist-assigned measures of quality. This analysis allows us to formulate a computable measure of quality specific to the artist and the generative system.…”