Quantifying the dynamics of particle suspensions is a widespread interest in soft matter. For instance, probing the motion of cells or larger organisms can help us understand biological behavior. When multiple particles interact, they perform collective dynamics, which visually translates into a zoology of effects. Yet, available analysis techniques face challenges reconstructing trajectories in dense or heterogeneous suspensions where accurately labelling particles is difficult. 

Inspired by Smoluchowski, we introduce a broadly applicable analysis technique, that probes particle dynamics based on a simple principle: counting the fluctuating number of particles in finite observation boxes of an image. Through colloidal experiments, simulations, and theory, we demonstrate the practical benefits of analyzing fluctuating counts. We can determine equilibrium motion properties, such as self-diffusion coefficients. Moreover, by increasing the observation box size, we can naturally probe collective diffusion coefficients. Out-of-equilibrium features also manifest in such fluctuating counts: for instance, our framework is sensitive to self-propulsion velocities and can distinguish between different reorientation dynamics. Beyond, by correlating nearby boxes we demonstrate how to map out flow field maps.

Both in dense or heterogeneous states, by simply counting particles, we overcome some of the challenges of trajectory reconstruction; and, more importantly open up the possibility of systematically linking individual and collective behavior, with broad perspectives in soft and statistical physics.