The present disclosure relates to systems, non-transitory computer-readable media, and methods that provide and apply dynamic image filters to modify digital images over time to simulate a dynamical system. Such dynamic image filters can modify a digital image to progress through different frames depicting visual effects mimicking natural and/or artificial qualities of a fluid, gas, chemical, cloud formation, fractal, or various physical matters or phenomena according to a dynamic-simulation function. Upon detecting a selection of a dynamic image filter, the disclosed systems can identify a dynamic-simulation function corresponding to the dynamical system. Based on selecting a portion of the (or entire) digital image at which to apply the dynamic image filter, the disclosed systems incrementally modify the digital image across time steps to simulate the dynamical system according to the dynamic-simulation function.