Through history to growth dynamics: deciphering the evolution of spatial networks

Stanisław Żukowski, Piotr Morawiecki, Hansjörg Seybold, Piotr Szymczak

Research output: Contribution to journalArticlepeer-review

1 Citation (SciVal)


Many ramified, network-like patterns in nature, such as river networks or blood vessels, form as a result of unstable growth of moving boundaries in an external diffusive field. Here, we pose the inverse problem for the network growth—can the growth dynamics be inferred from the analysis of the final pattern? We show that by evolving the network backward in time one can not only reconstruct the growth rules but also get an insight into the conditions under which branch splitting occurs. Determining the growth rules from a single snapshot in time is particularly important for growth processes so slow that they cannot be directly observed, such as growth of river networks and deltas or cave passages. We apply this approach to analyze the growth of a real river network in Vermont, USA. We determine its growth rule and argue that branch splitting events are triggered by an increase in the tip growth velocity.

Original languageEnglish
Article number20407
JournalScientific Reports
Issue number1
Early online date27 Nov 2022
Publication statusPublished - 31 Dec 2022

Bibliographical note

Funding Information:
This work was supported by the National Science Center (Poland) under research Grant No. 2016/21/B/ST3/01373. We would like to thank group of Daniel Rothman, MIT, and Olivier Devauchelle for the discussions and insightful remarks.

ASJC Scopus subject areas

  • General


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