Emergent Loewner Dynamics in Slime Mold Growth
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914384454877184 |
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| author | David, Claire Boussard, Aurèle Riane, Nizare Lapidus, Michel L. Dussutour, Audrey |
| author_facet | David, Claire Boussard, Aurèle Riane, Nizare Lapidus, Michel L. Dussutour, Audrey |
| contents | Growth fronts of slime molds are characterized through a direct geometric analysis based on Loewner evolutions, using experimentally acquired time-resolved images. The associated Loewner driving functions reconstructed from expanding pseudopod boundaries display statistical properties consistent with Gaussian-like behavior.
A geometric estimate of the diffusivity parameter~$κ$ is inferred from fractal scaling, while Brownian diagnostics are assessed on the reconstructed driving signal.
These findings show that the boundaries of a growing living organism display statistical and geometric properties consistent with emergent Loewner dynamics over experimentally accessible scales. This study establishes a quantitative framework for analyzing biological growth interfaces and suggests new connections between morphogenesis, stochastic geometry, and network reorganization under varying environmental conditions.
We provide, to our knowledge, the first explicit reconstruction of a Loewner driving function from a living growth interface, revealing an emergent Brownian-like conformal growth regime at expanding fronts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10201 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Emergent Loewner Dynamics in Slime Mold Growth David, Claire Boussard, Aurèle Riane, Nizare Lapidus, Michel L. Dussutour, Audrey Analysis of PDEs Mathematical Physics 28A75, 28A80, 35R02, 57Q70, 92C15, 92C80 Growth fronts of slime molds are characterized through a direct geometric analysis based on Loewner evolutions, using experimentally acquired time-resolved images. The associated Loewner driving functions reconstructed from expanding pseudopod boundaries display statistical properties consistent with Gaussian-like behavior. A geometric estimate of the diffusivity parameter~$κ$ is inferred from fractal scaling, while Brownian diagnostics are assessed on the reconstructed driving signal. These findings show that the boundaries of a growing living organism display statistical and geometric properties consistent with emergent Loewner dynamics over experimentally accessible scales. This study establishes a quantitative framework for analyzing biological growth interfaces and suggests new connections between morphogenesis, stochastic geometry, and network reorganization under varying environmental conditions. We provide, to our knowledge, the first explicit reconstruction of a Loewner driving function from a living growth interface, revealing an emergent Brownian-like conformal growth regime at expanding fronts. |
| title | Emergent Loewner Dynamics in Slime Mold Growth |
| topic | Analysis of PDEs Mathematical Physics 28A75, 28A80, 35R02, 57Q70, 92C15, 92C80 |
| url | https://arxiv.org/abs/2603.10201 |