Fractal Dimension of Bioconvection Patterns

Abstract

Shallow cultures of the motile algal strain, Euglena gracilis, were concentrated to 2×10⁶ organisms per ml and placed in constant temperature water baths at 24 and 38 C. Bioconvective patterns formed an open two-dimensional structure with random branches, similar to clusters encountered in the diffusion-limited aggregation (DLA) model. When averaged over several example cultures, the pattern was found to have no natural length scale, self-similar branching and a fractal dimension (d∼1.7). These agree well with the two-dimensional DLA.