I've been working a lot lately with both models and experiments concerning Brownian motion of microparticles in suspension and had a plot of particle trajectories that underwent a 2D random walk up on my computer screen. My officemate commented that it looked like the scribbles that her niece does with crayons and it got me thinking: can the scribble trajectories of children be modeled as some sort of random walk? I imagine it'll likely be anisotropic since they seem to scribble either primarily up-and-down or left-and-right. But it would be an interesting sociological study to try and correlate the statistics of the scribbles (fractal dimension, diffusion coefficient, etc.) with some societal factor.
Yes, this would likely be frivolous science but I'd find it fun anyway =)