The formation of molecular clusters is common in a wide variety of systems, such as fluids and gels, yet it is not fully understood. Shapes and sizes of these clusters determine important macroscopic properties of bulk matter, such as mechanical stability and electronic conductivity. The lifetime of these clusters is extremely long in gels, while it is very short in purely repulsive systems. The classical experimental techniques do not provide direct information regarding the distributions of shapes and sizes of these clusters; this limits theoretical understanding of this fundamental phenomenon.

We form two-dimensional suspensions of colloids, micro-spheres in a solvent; this models a simple atomic system. We vary the interactions in our system from hard-repulsive to short-ranged attractive, and measure the positions of our colloids by direct confocal microscopy.

To characterize the shapes of our clusters we measure their gyration radii; strikingly, while the largest clusters have a dimension of 2, the smallest clusters are best characterized by a fractal dimension of 1.6; we reproduce these results, employing a simple theoretical model. Further, we demonstrate that the size distribution of our clusters follows a power law; this behavior stays in contrast with the predictions of the common theoretical models.