A RandomWalk can be in any number of dimensions, but it is easiest to understand in one or two. Pick a direction at random and take a step. Then do it again.
The distance travelled is proportional to the square root of the time of the walk (number of steps). This is useful when considering gas diffusion and other physics problems.
In the context of thinking (now there's an interesting analogy!), a RandomWalk might be an inventory or perusal of cognitions without organization or structure. Perhaps this is related to the free-flowing word association game, whose name I forget?
Possible uses? BrainStorming springs to mind.
Pick a direction at random and take a step. Then do it again. Once I made a LogoWriter? program that did that moving a random distance each step. (Ed: This is called a Levy flight, and has different statistics.) It also changed the color randomly before each move. Another variant is to have it go to home after each iteration. -- RobertOrBob
Is FreeAssociation? a RandomWalk meaning what you think of next is a node "adjacent" to what you are thinking of now (even if the new point is picked randomly), or is completely random ie a point further away or arbitrary distance? Here I am assuming the knowledge is organized similar to a SemanticNet. By FreeAssociation? I mean thoughts that occur when not focusing on a problem or task (which require concentration on related nodes although the EurekaMoment might involve processes similar to FreeAssociation?).
See also: RandomPages, if you're after something random. It isn't much of a walk though.