Paintings, Polygons and Plant Propagation

  • Misha Paauw
  • Daan van den BergEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11453)


It is possible to approximate artistic images from a limited number of stacked semi-transparent colored polygons. To match the target image as closely as possible, the locations of the vertices, the drawing order of the polygons and the RGBA color values must be optimized for the entire set at once. Because of the vast combinatorial space, the relatively simple constraints and the well-defined objective function, these optimization problems appear to be well suited for nature-inspired optimization algorithms.

In this pioneering study, we start off with sets of randomized polygons and try to find optimal arrangements for several well-known paintings using three iterative optimization algorithms: stochastic hillclimbing, simulated annealing and the plant propagation algorithm. We discuss the performance of the algorithms, relate the found objective values to the polygonal invariants and supply a challenge to the community.


Paintings Polygons Plant propagation algorithm Simulated annealing Stochastic hillclimbing 



We would like to thank Abdellah Salhi (University of Essex) and Eric Fraga (University College London) for their unrelenting willingness to discuss and explain the plant propagation algorithm. A big thanks also goes to Arnoud Visser (University of Amsterdam) for providing some much-needed computing power towards the end of the project, and to Jelle van Assema for helping with the big numbers.


  1. 1.
    Roger Johansson blog: Genetic programming: Evolution of Mona Lisa.
  2. 2.
  3. 3.
    Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing, 1st edn. Springer, Heidelberg (2003). Scholar
  4. 4.
    Fister Jr., I., Yang, X.S., Fister, I., Brest, J., Fister, D.: A brief review of nature-inspired algorithms for optimization (2013). arXiv preprint: arXiv:1307.4186
  5. 5.
    Sörensen, K.: Metaheuristics—the metaphor exposed. Int. Trans. Oper. Res. 22, 1–16 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Mézard, M., Parisi, G., Zecchina, R.: Analytic and algorithmic solution of random satisfiability problems. Science 297(5582), 812–815 (2002)CrossRefGoogle Scholar
  7. 7.
    Mézard, M., Parisi, G.: The cavity method at zero temperature. J. Stat. Phys. 111(1–2), 1–34 (2003)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Kirkpatrick, S., Gelatt, C.D., Vecchi, M.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Hornby, G., Globus, A., Linden, D., Lohn, J.: Automated antenna design with evolutionary algorithms. In: Space, p. 7242 (2006)Google Scholar
  10. 10.
    Moshrefi-Torbati, M., Keane, A.J., Elliott, S.J., Brennan, M.J., Rogers, E.: Passive vibration control of a satellite boom structure by geometric optimization using genetic algorithm. J. Sound Vibr. 267(4), 879–892 (2003)CrossRefGoogle Scholar
  11. 11.
    Jelisavcic, M., et al.: Real-world evolution of robot morphologies: a proof of concept. Artif. Life 23(2), 206–235 (2017)CrossRefGoogle Scholar
  12. 12.
    Salhi, A., Fraga, E.: Nature-inspired optimisation approaches and the new plant propagation algorithm. In: Proceeding of the International Conference on Numerical Analysis and Optimization (ICeMATH 2011), Yogyakarta, Indonesia (2011)Google Scholar
  13. 13.
    Selamoğlu, Bİ., Salhi, A.: The plant propagation algorithm for discrete optimisation: the case of the travelling salesman problem. In: Yang, X.-S. (ed.) Nature-Inspired Computation in Engineering. SCI, vol. 637, pp. 43–61. Springer, Cham (2016). Scholar
  14. 14.
    Cheraita, M., Haddadi, S., Salhi, A.: Hybridizing plant propagation and local search for uncapacitated exam scheduling problems. Int. J. Serv. Oper. Manag. (in press).
  15. 15.
    Neumann, A., Alexander, B., Neumann, F.: Evolutionary image transition using random walks. In: Correia, J., Ciesielski, V., Liapis, A. (eds.) EvoMUSART 2017. LNCS, vol. 10198, pp. 230–245. Springer, Cham (2017). Scholar
  16. 16.
    Richter, H.: Visual art inspired by the collective feeding behavior of sand-bubbler crabs. In: Liapis, A., Romero Cardalda, J.J., Ekárt, A. (eds.) EvoMUSART 2018. LNCS, vol. 10783, pp. 1–17. Springer, Cham (2018). Scholar
  17. 17.
    Semet, Y., O’Reilly, U.-M., Durand, F.: An interactive artificial ant approach to non-photorealistic rendering. In: Deb, K. (ed.) GECCO 2004, Part I. LNCS, vol. 3102, pp. 188–200. Springer, Heidelberg (2004). Scholar
  18. 18.
    MacCallum, R.M., Mauch, M., Burt, A., Leroi, A.M.: Evolution of music by public choice. Proc. Natl. Acad. Sci. 109(30), 12081–12086 (2012)CrossRefGoogle Scholar
  19. 19.
    Python image library 5.1.0.
  20. 20. paintings, polygons, and plant propagation.
  21. 21.
    Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6, 721–741 (1984)CrossRefGoogle Scholar
  22. 22.
    Nourani, Y., Andresen, B.: A comparison of simulated annealing cooling strategies. J. Phys. A Math. Gen. 31, 8373–8385 (1998)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute for InformaticsUniversity of AmsterdamAmsterdamThe Netherlands

Personalised recommendations