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The Enigma of Complexity

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12693)

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.

Keywords

  • Complexity
  • Aesthetic measure
  • Generative art
  • Generative design
  • Evolutionary art
  • Fitness measure

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Notes

  1. 1.

    We adopted this measure as it specifically deals with complexity as defined in [22]. Machardo & Cardoso also define an aesthetic measure as the ratio of image complexity to processing complexity [20], as used by den Heijer & Eiben in their comparison of aesthetic measures [10].

  2. 2.

    Readers should not draw any direct relation between the terms “structural” and “physical” in relation to complexity used here. Structural refers to image structures, whereas physical refers to characteristics of the 3D form’s line segments.

References

  1. Barlow, P., Brain, P., Adam, J.: Differential growth and plant tropisms: a study assisted by computer simulation. In: Differential Growth in Plants, pp. 71–83. Elsevier (1989)

    Google Scholar 

  2. Berlyne, D.E.: Aesthetics and Psychobiology. Appleton-Century-Crofts, New York (1971)

    Google Scholar 

  3. Biederman, I.: Geon theory as an account of shape recognition in mind and brain. Irish J. Psychol. 14(3), 314–327 (1993)

    CrossRef  Google Scholar 

  4. Birkhoff, G.D.: Aesthetic Measure. Harvard University Press, Cambridge (1933)

    CrossRef  Google Scholar 

  5. Brunswik, E.: Perception and the Representative Design of Psychological Experiments, 2nd edn. University of California Press, Berkley and Los Angeles (1956)

    CrossRef  Google Scholar 

  6. Crutchfield, J.P.: Complexity: metaphors, models, and reality. In: Is Anything Ever New?: Considering Emergence, vol. XIX, pp. 479–497. Addison-Wesley, Redwood City (1994)

    Google Scholar 

  7. Forsythe, A., Nadal, M., Sheehy, N., Cela-Conde, C.J., Sawey, M.: Predicting beauty: fractal dimension and visual complexity in art. Br. J. Psychol. 102(1), 49–70 (2011)

    CrossRef  Google Scholar 

  8. Gell-Mann, M.: What is complexity? Complexity 1(1), 16–19 (1995)

    MathSciNet  CrossRef  Google Scholar 

  9. Greenfield, G.: On the origins of the term computational aesthetics. In: Neumann, L., Sbert, M., Gooch, B., Purgathofer, W. (eds.) Computational Aesthetics in Graphics, Visualization and Imaging, pp. 9–12. The Eurographics Association (2005). https://doi.org/10.2312/COMPAESTH/COMPAESTH05/009-012

  10. den Heijer, E., Eiben, A.E.: Comparing aesthetic measures for evolutionary art. In: Applications of Evolutionary Computation, pp. 311–320. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12242-2_32

  11. den Heijer, E., Eiben, A.E.: Comparing aesthetic measures for evolutionary art. In: European Conference on the Applications of Evolutionary Computation, pp. 311–320. Springer, Heidelberg (2010)

    Google Scholar 

  12. Hoenig, F.: Defining computational aesthetics. In: Neumann, L., Sbert, M., Gooch, B., Purgathofer, W. (eds.) Computational Aesthetics in Graphics, Visualization and Imaging. The Eurographics Association (2005). https://doi.org/10.2312/COMPAESTH/COMPAESTH05/013-018

  13. Jausovec, N., Jausovec, K.: Brain, creativity and education. Open Educ. J. 4, 50–57 (2011)

    CrossRef  Google Scholar 

  14. Johnson, C.G., McCormack, J., Santos, I., Romero, J.: Understanding aesthetics and fitness measures in evolutionary art systems. Complexity 2019 (Article ID 3495962), 14 pages (2019). https://doi.org/10.1155/2019/3495962

  15. Klinger, A., Salingaros, N.A.: A pattern measure. Environ. Plan. B: Plan. Design 27(4), 537–547 (2000)

    CrossRef  Google Scholar 

  16. Lakhal, S., Darmon, A., Bouchaud, J.P., Benzaquen, M.: Beauty and structural complexity. Phys. Rev. Research 2(2), 022058 (2020). https://doi.org/10.1103/PhysRevResearch.2.022058

    CrossRef  Google Scholar 

  17. Leder, H., Nadal, M.: Ten years of a model of aesthetic appreciation and aesthetic judgments: the aesthetic episode - developments and challenges in empirical aesthetics. Br. J. Psychol. 105, 443–464 (2014)

    CrossRef  Google Scholar 

  18. Lomas, A.: Species explorer: an interface for artistic exploration of multi-dimensional parameter spaces. In: Bowen, J., Lambert, N., Diprose, G. (eds.) Electronic Visualisation and the Arts (EVA 2016). Electronic Workshops in Computing (eWiC), BCS Learning and Development Ltd., London, 12th–14th July 2016

    Google Scholar 

  19. Lomas, A.: On hybrid creativity. Arts 7(3), 25 (2018). https://doi.org/10.3390/arts7030025

    CrossRef  Google Scholar 

  20. Machado, P., Cardoso, A.: Computing aesthetics. In: de Oliveira, F.M. (ed.) SBIA 1998. LNCS (LNAI), vol. 1515, pp. 219–228. Springer, Heidelberg (1998). https://doi.org/10.1007/10692710_23

    CrossRef  Google Scholar 

  21. Machado, P., Romero, J., Nadal, M., Santos, A., Correia, J., Carballa, A.: Computerized measures of visual complexity. Acta Psychol. 160, 43–57 (2015). https://doi.org/10.1016/j.actpsy.2015.06.005

    CrossRef  Google Scholar 

  22. Machado, P., Romero, J., Nadal, M., Santos, A., Correia, J., Carballal, A.: Computerized measures of visual complexity. Acta psychol. 160, 43–57 (2015)

    CrossRef  Google Scholar 

  23. McCormack, J.: Open problems in evolutionary music and art. In: Rothlauf, F., et al. (eds.) EvoWorkshops 2005. LNCS, vol. 3449, pp. 428–436. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-32003-6_43

    CrossRef  Google Scholar 

  24. McCormack, J.: Enhancing creativity with niche construction. In: Fellerman, H., et al. (eds.) Artificial Life XII, pp. 525–532. MIT Press, Cambridge (2010)

    Google Scholar 

  25. McCormack, J.: Niche Constructions Generative Art Dataset, January 2021. https://bridges.monash.edu/articles/dataset/Niche_Constructions_Generative_Art_Dataset/13662383

  26. McCormack, J., Bown, O.: Life’s what you make: Niche construction and evolutionary art. In: Giacobini, M., et al. (eds.) EvoWorkshops 2009. LNCS, vol. 5484, pp. 528–537. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01129-0_59

    CrossRef  Google Scholar 

  27. McCormack, J., Gambardella, C.C.: DLA Form Generation dataset, January 2021. https://doi.org/10.26180/13663400.v1. https://bridges.monash.edu/articles/dataset/DLA_Form_Generation_dataset/13663400

  28. McCormack, J., Lomas, A.: Andy Lomas generative art dataset. https://doi.org/10.5281/zenodo.4047222

  29. McCormack, J., Lomas, A.: Deep learning of individual aesthetics. Neural Comput. Appl. 33(1), 3–17 (2020). https://doi.org/10.1007/s00521-020-05376-7

    CrossRef  Google Scholar 

  30. Papadimitriou, F.: Spatial complexity, visual complexity and aesthetics. Spatial Complexity, pp. 243–261. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-59671-2_16

    CrossRef  Google Scholar 

  31. Peitgen, H.O., Richter, P.H.: The Beauty of Fractals: Images of Complex Dynamical Systems. Springer, Berlin (1986). https://doi.org/10.1007/978-3-642-61717-1

    CrossRef  MATH  Google Scholar 

  32. Prigogine, I.: From Being to Becoming: Time and Complexity in the Physical Sciences. W. H. Freeman, New York (1980)

    Google Scholar 

  33. Skov, M.: Aesthetic appreciation: the view from neuroimaging. Empirical Stud. Arts 37(2), 220–248 (2019). https://doi.org/10.1177/0276237419839257

    CrossRef  Google Scholar 

  34. Spehar, B., Clifford, C.W.G., Newell, B.R., Taylor, R.P.: Universal aesthetic of fractals. Comput. Graph. 27(5), 813–820 (2003)

    CrossRef  Google Scholar 

  35. Sun, L., Yamasaki, T., Aizawa, K.: Relationship between visual complexity and aesthetics: application to beauty prediction of photos. In: Agapito, L., Bronstein, M.M., Rother, C. (eds.) ECCV 2014. LNCS, vol. 8925, pp. 20–34. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-16178-5_2

    CrossRef  Google Scholar 

  36. Taylor, R.P., Micolich, A.P., Jonas, D.: Fractal analysis of Pollock’s drip paintings. Nature 399, 422 (1999)

    CrossRef  Google Scholar 

  37. Wolfram, S.: A New Kind of Science. Wolfram Media, Champaign (2002)

    MATH  Google Scholar 

  38. Zanette, D.H.: Quantifying the complexity of black-and-white images. PLoS ONE 13(11), e0207879 (2018). https://doi.org/10.1371/journal.pone.0207879

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McCormack, J., Cruz Gambardella, C., Lomas, A. (2021). The Enigma of Complexity. In: Romero, J., Martins, T., Rodríguez-Fernández, N. (eds) Artificial Intelligence in Music, Sound, Art and Design. EvoMUSART 2021. Lecture Notes in Computer Science(), vol 12693. Springer, Cham. https://doi.org/10.1007/978-3-030-72914-1_14

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  • DOI: https://doi.org/10.1007/978-3-030-72914-1_14

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