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Here are some pictures of the objects that I work with.

 

particle2
Evolving particle paths in the Brownian conga line.

 

congasimulate
The Brownian conga line for 10,000 steps (red) and 9900 steps (blue). (courtesy: Krzysztof Burdzy).

 

reflectioncoupling
Reflection coupling of two Brownian motions (courtesy: Wilfrid Kendall)
Gravitation versus Brownian motion (courtesy: Mauricio Duarte)
Gravitation versus Brownian motion. Blue: path of inert particle, red: path of Brownian particle, black: gap between particles, green: velocity of inert particle. (courtesy: Mauricio Duarte)

 

heisenberg-ball
Unit ball in the Heisenberg group (taken from “An introduction to the geometry of stochastic flows” by Fabrice Baudoin).