Brownian Motion - Visual Scaling in the Plane

Pictured here on the left is a portion of the trail left by a particle undergoing Brownian motion in the plane.
To emphasize the scaling of Brownian trails, the first quarter of the trail is contained in the box on the left.
This box is magnified by a factor of 2 (horizontally and vertically) to give the box on the right, and the first quarter of the left trail is rescaled within this box.
(Later parts of the first trail reenter this box, so some of the parts shown on the left box are not shown in the right box.)
More detail is revealed in the magnification, and the left side and right side look very similar.
Note we have scaled the time by a factor of 4 (first quarter), and space by a factor of 2. We shall see this relation is central to Brownian motion.

Return to Brownian motion.