Study of surface morphology complexity of Bacillus subtilis biofilms by coarse-graining method at different size scales.

Biofilms develop highly undulating three-dimensional morphologies that are often described as fractal. However, in biofilm studies, conventional fractal analyses have often relied on two-dimensional grayscale projections or single-value descriptors, which may obscure how surface morphology varies across spatial scales. Here, using Bacillus subtilis biofilms, we apply a voxel-based coarse-graining approach in which biofilm thickness is reconstructed from transmitted-light optical density using a Beer-Lambert law, and normalized exposed-surface-area trajectories are obtained across prescribed spatial scales. Notably, biofilms with identical fractal dimensions DFL from conventional 2D box-counting exhibit distinct exposed surface area trajectories, indicating that area-versus-scale analysis of reconstructed biofilm surfaces can reveal multiscale differences not resolved by a single fractal dimension. With increasing nutrient concentration, the area scale fractal dimension DA decreased and prominent large-scale folds were reduced, whereas biofilm aging increased surface complexity and increased the relative contribution of small-scale features relative to large-scale structures. This provides a complementary approach to quantifying biofilm surface structure beyond conventional two-dimensional fractal analysis.