Self-organized 3D-Printing Patterns Simulated by Cellular Automata

  • Yasusi Kanada
Part of the Mathematics for Industry book series (MFI, volume 14)


3D printers are usually used for printing objects designed by 3D CAD exactly, i.e., deterministically. However, 3D printing process contains stochastic self-organization process that generate emergent patterns. A method for generating fully self-organized patterns using a fused deposition modeling (FDM) 3D printer has been developed. Melted plastic filament is extruded constantly in this method; however, by using this method, various patterns, such as stripes, splitting and/or merging patterns, and meshes can be generated. A cellular-automata-based computational model that can simulate such patterns have also been developed.


3D printing Asynchronous cellular automata (CA) Randomness Fluctuation Fused deposition modeling (FDM) 


  1. Creating naturally-fluctuated patterns using a 3D printer. YouTube.
  2. Gibson, I., Rosen, D.W., Stucker, B.: Additive manufacturing technologies. Springer (2010)Google Scholar
  3. Hofmann, M.I.: A cellular automaton model based on cortical physiology. Complex Syst. 1, 187–202 (1987)Google Scholar
  4. Ingerson, T.E., Buvel, R.L.: Structure in asynchronous cellular automata. Phys. D 10, 59–68 (1984)MathSciNetCrossRefGoogle Scholar
  5. Kanada, Y.: The Effects of randomness in asynchronous 1D cellular automata. Artificial Life IV (Unpublished extended version. (1994)
  6. Kanada, Y.: 3D printing and simulation of naturally-randomized cellular-automata. Artif Life and Robot. 19, 311–316 (2014)Google Scholar
  7. RepRap Wiki (2015).
  8. Asynchronous cellular automaton. Wikipedia.
  9. Wolfram, S.: Universality and complexity in cellular automata. Phys. D 10, 1–35 (1984)Google Scholar

Copyright information

© Springer Japan 2016

Authors and Affiliations

  1. 1.Dasyn.comTokyoJapan

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