Arc-Length Characterization of Finite, Radial Growth Patterns

We present a method to characterize the distribution of length scales of finite, disordered patterns with, on average, radial symmetry. This method makes it possible to quantify the distribution of characteristic length scales in cases where the conventional "linear" chord method does not work. We show that the method can clearly distinguish regular patterns, patterns that are formed by diffusion-limited aggregation, and patterns that form during the slow drying of confined, colloid-laden droplets. We also introduce a method to find the center point of these finite patterns without assuming full connectivity in the pattern. The method should be widely applicable to other finite, quasi-two-dimensional patterns, like dendritic structures, viscous fingering, liquid crystal patterns, and bacterial growth.