Mathematical model for worm path simulation in 3D
- 1Department of Clinical and Biomedical Sciences (CBS), University of Exeter, Exeter, United Kingdom
Abstract
This research presents the evaluation of a computer simulation for modelling shapes of paths traversed by various artificial species of worm on a 3D orthogonal grid. These resulting 3D worm trace patterns have not been modelled or analysed before. Simulation software was custom developed in multiple programming languages and platforms, supporting 3D graphics and virtual reality visualisations on various headsets and operating systems. A genetic encoding enables exploration of the full range of 3D worm phenotypes, this research modelled every possible unique worm in simulations up to 53.5 million time-steps. The results show that in this new 3D grid, there are 3239 potentially unique worms. Of the 3239 unique worms, 1882 (58%) terminated at the origin. Also 1352 (41%) of worms entered repeating loops, some complex loops were identified with lengths of up to 296639. Currently 5 worms (0.1%) continue to run chaotically beyond 53.5 million population in simulation runs, and their final outcome still has not been identified yet and remains unknown. Simple rules result in surprisingly complex and intricate movements. Images and unique outlier observations are presented demonstrating complex 3D patterns that emerge.
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BibTeX
@article{vaughan2026mathematical,
title = {{Mathematical model for worm path simulation in 3D}},
author = {Neil Vaughan},
journal = {PLOS One},
year = {2026},
month = sep,
doi = {10.1371/journal.pone.0358065},
url = {https://doi.org/10.1371/journal.pone.0358065},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Mathematical model for worm path simulation in 3D
AU - Neil Vaughan
PY - 2026
DA - 2026/09/11
JO - PLOS One
DO - 10.1371/journal.pone.0358065
UR - https://doi.org/10.1371/journal.pone.0358065
AB - This research presents the evaluation of a computer simulation for modelling shapes of paths traversed by various artificial species of worm on a 3D orthogonal grid. These resulting 3D worm trace patterns have not been modelled or analysed before. Simulation software was custom developed in multiple programming languages and platforms, supporting 3D graphics and virtual reality visualisations on various headsets and operating systems. A genetic encoding enables exploration of the full range of 3D worm phenotypes, this research modelled every possible unique worm in simulations up to 53.5 million time-steps. The results show that in this new 3D grid, there are 3239 potentially unique worms. Of the 3239 unique worms, 1882 (58%) terminated at the origin. Also 1352 (41%) of worms entered repeating loops, some complex loops were identified with lengths of up to 296639. Currently 5 worms (0.1%) continue to run chaotically beyond 53.5 million population in simulation runs, and their final outcome still has not been identified yet and remains unknown. Simple rules result in surprisingly complex and intricate movements. Images and unique outlier observations are presented demonstrating complex 3D patterns that emerge.
SN - 1932-6203
ER -