A preference for some types of complexity comment on “perceived beauty of random texture patterns: A preference for complexity” Nicolas Gauvrit a, ⁎, Fernando Soler-Toscano b , Alessandro Guida c a Human and artificial Cognition Lab, EPHE, Paris, France b University of Seville, Spain c LP3C, University of Rennes 2, France abstract article info Article history: Received 6 October 2016 Received in revised form 19 January 2017 Accepted 23 January 2017 Available online xxxx In two experiments, Friedenberg and Liby (2016) studied how a diversity of complexity estimates such as density, number of blocks, GIF compression rate and edge length impact the perception of beauty of semi- random two-dimensional patterns. They concluded that aesthetics ratings are positively linked with GIF compression metrics and edge length, but not with the number of blocks. They also found an inverse U-shaped link between aesthetic judgments and density. These mixed results originate in the variety of metrics used to es- timate what is loosely called “complexity” in psychology and indeed refers to conflicting notions. Here, we rean- alyze their data adding two more conventional and normative mathematical measures of complexity: entropy and algorithmic complexity. We show that their results can be interpreted as an aesthetic preference for low re- dundancy, balanced patterns and “crooked” figures, but not for high algorithmic complexity. We conclude that participants tend to have a preference for some types of complexity, but not for all. These findings may help un- derstand divergent results in the study of perceived beauty and complexity, and illustrate the need to specify the notion of complexity used in psychology. The field would certainly benefit from a precise taxonomy of complex- ity measures. © 2017 Elsevier B.V. All rights reserved. Keywords: Complexity Aesthetics Random patterns Entropy Algorithmic information theory Algorithmic complexity 1. Introduction Within the long-standing line of research investigating the human judgment of beauty (Berlyne, 1971; Birkhoff, 1932; Eysenck, 1940), complexity has been a prominent issue with contradictory conclusions (for a brief review see Forsythe, Nadal, Sheehy, Cela-Conde & Sawey, 2011). We believe that two factors contribute to this heterogeneity (for a similar view see Nadal, Munar, Marty & Cela-Conde, 2010). Firstly, many studies on the per- ception of beauty have used pictures, paintings, portraits or natural world objects to increase ecological validity (e.g., Krupinski & Locher, 1988; Messinger, 1998; Nicki, Lee, & Moss, 1981; Osborne & Farley, 1970). By doing so, they have introduced unwanted confounding factors. Studies based on more abstract stimuli are probably easier to interpret. In this respect, experiments based on non figurative material (Aitken, 1974; Ichikawa, 1985; Markovic & Gvozdenovic, 2001), such as two-dimensional binary grids (i.e., grids with black and white cells, e.g., Palumbo, Ogden, Makin, & Bertamini, 2014; Spehar, Clifford, Newell, & Taylor, 2003; Bertamini, Makin, & Pecchinenda, 2013), are of special interest as they are easily modeled in a mathematical sound way as binary ma- trices, which gives access to well-defined measures of complexity. Secondly, what is exactly meant by “complexity” is variable from one study to another, as many definitions of complexity exist. This is problematic as different types of complexity might result in differ- ent outcomes. In a recent paper, Friedenberg and Liby (2016) investigated how participants rate the beauty of artificial 2-dimensional binary grids for various levels of complexity. The authors used different indices of complexity, listed below: • The number of parts or blocks in the pattern (a block is a maximal subset of adjacent black cells; see Appendix for examples). • The total edge length, which is the perimeter of the figure defined by the black cells (see Appendix for examples). • The GIF compression metrics, defined as GIF/BMP where “GIF” is the size of the image file in GIF format and “BMP” the size of the BMP image file of a given grid. BMP is a non-compressed format, and GIF is a lossless compressed format based on the Lempel-Ziv-Welch Acta Psychologica 174 (2017) 48–53 ⁎ Corresponding author. E-mail address: ngauvrit@me.com (N. Gauvrit). http://dx.doi.org/10.1016/j.actpsy.2017.01.007 0001-6918/© 2017 Elsevier B.V. All rights reserved. Contents lists available at ScienceDirect Acta Psychologica journal homepage: www.elsevier.com/locate/actpsy