Sloe gin and a random walk

I've been making sloe gin. You dissolve a large amount of sugar in half a bottle of gin and add sloes. Here it is after the first night. Look at how the red colouring has started to diffuse up the tube. Diffusion is the movement of particles from where they are most concentrated to where they are least concentrated down the concentration gradient. It works because of the random motion of the particles. In fact, they can be modelled using a dice with each number suggesting one of six directions. For each single molecule, the resultant path is called a random walk - or the walk of a drunk, perhaps after consuming too much sloe gin. But if you have millions of particles close together, the overall effect of these individual random walks is a spreading of the colour. I'm now at the stage of shaking the bottle every couple of days which spoils the effect but will give me a nice drink at Christmas!