System size and boundaries determine the patterning dynamics of attracting active particles

Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the collective dynamics of active self-attracting particles. We identify a sequence of size-controlled transitions that generate characteristic slow modes, leading to exponential increase of patterning timescales. Experimental measurements of multicellular dynamics confirm our predictions.