# On the growth of non-motile bacteria colonies: an agent-based model for pattern formation

## TL;DR

This paper introduces an off-lattice agent-based model for non-motile bacterial colony growth, capturing diverse pattern formations and analyzing their scaling and multifractal properties, advancing understanding beyond traditional lattice-based models.

## Contribution

It presents a novel off-lattice simulation approach for bacterial colonies, revealing pattern formation mechanisms and scaling laws not addressed by previous models.

## Key findings

- Simulated a wide range of colony morphologies matching experimental patterns.
- Identified a scaling relationship between interface and total cell numbers.
- Analyzed multifractal properties to characterize screening effects in growth patterns.

## Abstract

In the growth of bacterial colonies, a great variety of complex patterns are observed in experiments, depending on external conditions and the bacterial species. Typically, existing models employ systems of reaction-diffusion equations or consist of growth processes based on rules, and are limited to a discrete lattice. In contrast, the two-dimensional model proposed here is an off-lattice simulation, where bacteria are modelled as rigid circles and nutrients are point-like, Brownian particles. Varying the nutrient diffusion and concentration, we simulate a wide range of morphologies compatible with experimental observations, from round and compact to extremely branched patterns. A scaling relationship is found between the number of cells in the interface and the total number of cells, with two characteristic regimes. These regimes correspond to the compact and branched patterns, which are exhibited for sufficiently small and large colonies, respectively. In addition, we characterise the screening effect observed in the structures by analysing the multifractal properties of the growth probability.