Self-organized criticality and pattern emergence through the lens of tropical geometry

N. Kalinin, A. Guzmán-Sáenz, Y. Prieto, M. Shkolnikov, V. Kalinina, E. Lupercio*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


Tropical geometry, an established field in pure mathematics, is a place where string theory, mirror symmetry, computational algebra, auction theory, and so forth meet and influence one another. In this paper, we report on our discovery of a tropical model with self-organized criticality (SOC) behavior. Our model is continuous, in contrast to all known models of SOC, and is a certain scaling limit of the sandpile model, the first and archetypical model of SOC. We describe how our model is related to pattern formation and proportional growth phenomena and discuss the dichotomy between continuous and discrete models in several contexts. Our aim in this context is to present an idealized tropical toy model (cf. Turing reaction-diffusion model), requiring further investigation.

Original languageEnglish
Pages (from-to)E8135-E8142
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number35
StatePublished - 2018
Externally publishedYes


  • Pattern formation
  • Power laws
  • Proportional growth
  • Self-organized criticality
  • Tropical geometry


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