On Symmetry, Aesthetics and Quantifying Symmetrical Complexity

  • Mohammad Majid al-RifaieEmail author
  • Anna Ursyn
  • Robert Zimmer
  • Mohammad Ali Javaheri Javid
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10198)


The concepts of order and complexity and their quantitative evaluation have been at the core of computational notion of aesthetics. One of the major challenges is conforming human intuitive perception and what we perceive as aesthetically pleasing with the output of a computational model. Informational theories of aesthetics have taken advantage of entropy in measuring order and complexity of stimuli in relation to their aesthetic value. However entropy fails to discriminate structurally different patterns in a 2D plane. In this work, following an overview on symmetry and its significance in the domain of aesthetics, a nature-inspired, swarm intelligence technique (Dispersive Flies Optimisation or DFO) is introduced and then adapted to detect symmetries and quantify symmetrical complexities in images. The 252 Jacobsen & Höfel’s images used in this paper are created by researchers in the psychology and visual domain as part of an experimental study on human aesthetic perception. Some of the images are symmetrical and some are asymmetrical, all varying in terms of their aesthetics, which are ranked by humans. The results of the presented nature-inspired algorithm is then compared to what humans in the study aesthetically appreciated and ranked. Whilst the authors believe there is still a long way to have a strong correlation between a computational model of complexity and human appreciation, the results of the comparison are promising.


Human aesthetic perception Symmetry and complexity Aesthetics Swarm intelligence Dispersive flies optimisation 



We are grateful to Thomas Jacobsen of Helmut Schmidt University for granting permission to use his experimental stimuli.


  1. 1.
    al-Rifaie, M.M.: Dispersive flies optimisation. In: Ganzha, M., Maciaszek, L., Paprzycki, M. (eds.): Proceedings of the 2014 Federated Conference on Computer Science and Information Systems. Annals of Computer Science and Information Systems, vol. 2, pp. 529–538. IEEE (2014).
  2. 2.
    al-Rifaie, M.M., Aber, A.: Dispersive flies optimisation and medical imaging. In: Fidanova, S. (ed.) Recent Advances in Computational Optimization. Studies in Computational Intelligence, vol. 610, pp. 183–203. Springer, Heidelberg (2016)CrossRefGoogle Scholar
  3. 3.
    al-Rifaie, M.M., Leymarie, F.F., Latham, W., Bishop, M.: Swarmic autopoiesis and computational creativity. Connection Sci., 1–19 (2017).
  4. 4.
    Bauerly, M., Liu, Y.: Computational modeling and experimental investigation of effects of compositional elements on interface and design aesthetics. Int. J. Man Mach. Stud. 64(8), 670–682 (2006)Google Scholar
  5. 5.
    Behrens, R.: Design in the Visual Arts. Prentice-Hall, Upper Saddle River (1984)Google Scholar
  6. 6.
    Bennett, C., Ryall, J., Spalteholz, L., Gooch, A.: The aesthetics of graph visualization. Comput. Aesthetics 2007, 57–64 (2007)Google Scholar
  7. 7.
    Birkhoff, G.D.: Aesthetic Measure. Harvard University Press, Cambridge (1933)CrossRefzbMATHGoogle Scholar
  8. 8.
    Carroll, J.M. (ed.): HCI Models, Theories, and Frameworks Toward a Multidisciplinary Science. Morgan Kaufmann Publishers, San Francisco (2003)Google Scholar
  9. 9.
    Cheetham, M.A.: The crystal interface in contemporary art: metaphors of the organic and inorganic. Leonardo 43(3), 250–255 (2010)CrossRefGoogle Scholar
  10. 10.
    Dawkins, R.: The Blind Watchmaker. Norton & Company, Inc., New York (1986)Google Scholar
  11. 11.
    Ferreira, M.I.A.: Interactive bodies: The semiosis of architectural forms. Biosemiotics 5(2), 269–289 (2012)CrossRefGoogle Scholar
  12. 12.
    Galanter, P.: Complexity, neuroaesthetics, and computational aesthetic evaluation. In: 13th International Conference on Generative Art (GA2010) (2010)Google Scholar
  13. 13.
    Galanter, P.: Computational aesthetic evaluation: past and future. In: McCormack, J., d’Inverno, M. (eds.) Computers and Creativity, pp. 255–293. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    Gangestad, S.W., Thornhill, R., Yeo, R.A.: Facial attractiveness, developmental stability, and fluctuating asymmetry. Ethol. Sociobiol. 15(2), 73–85 (1994)CrossRefGoogle Scholar
  15. 15.
    Gaviria, A.R.: When is information visualization art? determining the critical criteria. Leonardo 41(5), 479–482 (2008)CrossRefGoogle Scholar
  16. 16.
    Jacobsen, T., Hofel, L.: Aesthetic judgments of novel graphic patterns: analyses of individual judgments. Percept. Mot. Skills 95(3), 755–766 (2002)CrossRefGoogle Scholar
  17. 17.
    Javid, M.A.J., Blackwell, T., Zimmer, R., al-Rifaie, M.M.: Correlation between human aesthetic judgement and spatial complexity measure. In: Johnson, C., Ciesielski, V., Correia, J., Machado, P. (eds.) EvoMUSART 2016. LNCS, vol. 9596, pp. 79–91. Springer, Cham (2016). doi: 10.1007/978-3-319-31008-4_6 CrossRefGoogle Scholar
  18. 18.
    Jiang, H., Ngo, C.W., Tan, H.K.: Gestalt-based feature similarity measure in trademark database. Pattern Recogn. 39(5), 988–1001 (2006)CrossRefGoogle Scholar
  19. 19.
    Kettle, S.F.: Symmetry and Structure: Readable Group Theory for Chemists. Wiley, New York (2008)Google Scholar
  20. 20.
    Lau, A., Moere, A.V.: Towards a model of information aesthetics in information visualization. In: 2007 11th International Conference on Information Visualization, IV 2007, pp. 87–92. IEEE (2007)Google Scholar
  21. 21.
    Lévi-Strauss, C.: Look, Listen, Learn. Translated by Singer, B.C.J.: Basic Books, a division of Harper-Collins Publishers (1997). ISBN 0465068804Google Scholar
  22. 22.
    Lewis, M.: Evolutionary visual art and design. In: Romero, J., Machado, P. (eds.) The Art of Artificial Evolution. Natural Computing Series, pp. 3–37. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  23. 23.
    Leyton, M.: Symmetry, Causality, Mind. Bradford Books/MIT Press, Cambridge (1992)Google Scholar
  24. 24.
    Liu, Y.: Computational Symmetry. CMU Robotics Institute (2000)Google Scholar
  25. 25.
    McCormack, J.: Interactive evolution of L-system grammars for computer graphics modelling. In: Complex Systems: From Biology to Computation, pp. 118–130 (1993)Google Scholar
  26. 26.
    Møller, A.P., Cuervo, J.J.: Asymmetry, size and sexual selection: meta-analysis, publication bias and factors affecting variation in relationships, p. 1. Oxford University Press (1999)Google Scholar
  27. 27.
    Møller, A.P., Thornhill, R.: Bilateral symmetry and sexual selection a meta-analysis. Am. Nat. 151(2), 174–192 (1998)Google Scholar
  28. 28.
    Onians, J.: Neuroarthistory: From Aristotle and Pliny to Baxandall and Zeki. Yale University Press, New Haven (2007)Google Scholar
  29. 29.
    Park, I.K., Lee, K.M., Lee, S.U.: Perceptual grouping of line features in 3-D space: A model-based framework. Pattern Recogn. 37(1), 145–159 (2004)CrossRefzbMATHGoogle Scholar
  30. 30.
    Purchase, H.C.: Metrics for graph drawing aesthetics. J. Vis. Lang. Comput. 13(5), 501–516 (2002)CrossRefGoogle Scholar
  31. 31.
    Purchase, H.C., Plimmer, B., Baker, R., Pilcher, C.: Graph drawing aesthetics in user-sketched graph layouts. In: Proceedings of the Eleventh Australasian Conference on User Interface, vol. 106, pp. 80–88. Australian Computer Society, Inc. (2010)Google Scholar
  32. 32.
    Railton, P.: Aesthetic value, moral value and the ambitions of naturalism. In: Aesthetics and Ethics, chap. 3. University of Maryland (2001)Google Scholar
  33. 33.
    Randy, T., Steven, G.: Human facial beauty. Hum. Nat. 4, 237–269 (1993)CrossRefGoogle Scholar
  34. 34.
    Rankin, D.W., Mitzel, N., Morrison, C.: Structural Methods in Molecular Inorganic Chemistry. Wiley, New York (2013)Google Scholar
  35. 35.
    Senyuk, B., Liu, Q., He, S., Kamien, R.D., Kusner, R.B., Lubensky, T.C., Smalyukh, I.I.: Topological colloids. Nature 493(7431), 200–205 (2013)CrossRefGoogle Scholar
  36. 36.
    Shackelford, T.K., Larsen, R.J.: Facial symmetry as an indicator of psychological emotional and physiological distress. J. Pers. Soc. Psychol. 72(2), 456–466 (1997)CrossRefGoogle Scholar
  37. 37.
    Sims, K.: Evolving virtual creatures. In: Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques, pp. 15–22. ACM (1994)Google Scholar
  38. 38.
    Stanley, W.: Crystalline tobacco-mosaic virus protein. Am. J. Bot. 24(2), 59–68 (1937)CrossRefGoogle Scholar
  39. 39.
    Todd, S., Latham, W., Hughes, P.: Computer sculpture design and animation. J. Visual. Comput. Anim. 2(3), 98–105 (1991)CrossRefGoogle Scholar
  40. 40.
    Ware, C., Purchase, H., Colpoys, L., McGill, M.: Cognitive measurements of graph aesthetics. Inf. Visual. 1(2), 103–110 (2002)CrossRefGoogle Scholar
  41. 41.
    Zeki, S., Nash, J.: Inner Vision: An Exploration of Art and the Brain, vol. 415. Oxford University Press, Oxford (1999)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Mohammad Majid al-Rifaie
    • 1
    Email author
  • Anna Ursyn
    • 2
  • Robert Zimmer
    • 1
  • Mohammad Ali Javaheri Javid
    • 1
  1. 1.GoldsmithsUniversity of LondonLondonUK
  2. 2.University of Northern ColoradoGreeleyUSA

Personalised recommendations