Summary

Biological pattern formation is one of the complex system phenomena in nature, requiring theoretical analysis based on mathematical modeling and computer simulations for in-depth understanding. We propose a Python framework named LPF to systematically explore the highly diverse wing color patterns of ladybirds using reaction-diffusion models. LPF supports GPU-accelerated array computing for numerical analysis of partial differential equation models, concise visualization of ladybird morphs, and evolutionary algorithms for searching mathematical models with deep learning models for computer vision.

Availability and implementation

LPF is available on GitHub at https://github.com/cxinsys/lpf.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.