I stumbled on this "painterly" effect while working on making fractal field visualizations with Trapcode Particular. I was using a quite large and dense Grid emitter, and tracing the particles' motion in the field by emitting aux particles:
I wanted to see how it would look with some colours and changed the Grid emitter into a Layer Grid emitter and placed a photo as source texture for the emitter. Here are two before/after for the effect:
There are no post effects added here, the pattern that reminds of a canvas is actually from the grid emitter. At first the particles are unaffected by the field, due to Turbulence>Fade In Time, and as time progresses they get more and more affected, leaving the aux trail all the way back to the original grid.
Here's what the build-up sequence looks like:
Download the After Effects project file and try it with your own images! Painterly.aep
By further boosting contrast (Brightness & Contrast effect) and adding Sharpen and Color Emboss the image looks even more like an oil painting on canvas: