Walkers on a field
Every point of the square carries a direction, shown by the faint ticks. A random walker ignores it and wanders. A ridge-following walker steps along the local direction, so its trail traces the flow lines of the field. Slide between the two and watch structure appear out of noise.
Field
Walkers
A random walker's distance from its start grows like √t. A follower's grows like t until the field curves it back.