Skip to main content

The Enigma of Complexity

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

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)

    Article  Google Scholar 

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

    Book  Google Scholar 

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

    Book  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)

    Article  Google Scholar 

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

    Article  MathSciNet  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)

    Article  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)

    Article  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

    Article  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)

    Article  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

    Article  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

    Chapter  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

    Article  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)

    Article  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

    Chapter  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

    Chapter  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

    Article  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

    Chapter  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

    Book  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

    Article  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)

    Article  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

    Chapter  Google Scholar 

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

    Article  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

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jon McCormack .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-72913-4

  • Online ISBN: 978-3-030-72914-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics