ARTST 122 Visual Design through Algorithms


Noboru Matsuo



Controlled Randomness: Brownian Motion

Brownian Motion refers to the random walk motion of small particles susupended in a fluid due to bombardment by molecules. The phenomenon was first observed by Jan Ingenhousz in 1785, but was subsequently rediscovered by Scottish botanist Robert Brown in 1828 (Weisstein). Brown observed the zigzag, irregular motion of pollen that was suspended in water. The effect has been observed in all types of colloidal suspensions, solid-in-liquid, liquid-in-liquid, gas-in-liquid, solid-in-gas, and liquid-in-gas (Bartleby).

The effect, being independent of all external factors, is ascribed to the thermal motion of the molecules of the fluid. These molecules are in constant irregular motion with a velocity proportional to the square root of the temperature. Brownian motion is observed for particles about 0.001 mm in diameter; these are small enough to share in the thermal motion, yet large enough to be seen with a microscope (Bartleby).

In 1905, Albert Einstein used kinetic theory to derive the diffusion constant for each motion in terms of fundamental parameters of the particles and liquid, and this equation was subsequently confirmed by Jean Perrin and was used to determine Avogadro's Number, 6.022 x 10^23, a constant of molecules in the same volume of any gas (Weisstein).

"There are two meanings of the term Brownian motion: the physical phenomenon that minute particles immersed in a fluid will experience a random movement, and one of the mathematical models used to describe it.

"The mathematical model can also be used to describe many phenomena not resembling (other than mathematically) the random movement of minute particles. An often quoted example is stock market fluctuations, and another important example is the evolution of physical characteristics in the fossil record.

"Brownian motion is the simplest stochastic process on a continuous domain, and it is a limit of both simpler (see random walk) and more complicated stochastic processes. This universality is closely related to the universality of the normal distribution. In both cases, it is often mathematical convenience rather than actual accuracy as models that dictates their use. All three quoted examples of Brownian motion are cases of this: it has been argued that Levy flights are a more accurate, if still imperfect, model of stock-market fluctuations; the physical Brownian motion can be modelled more accurately by more general diffusion process; and the dust hasn't settled yet on what the best model for the fossil record is, even after correcting for non-gaussian data (Fact Index)."

In the arts, as in nature, employing the rules of Brownian motion results in the controlled randomness as manifested in the examples below.

American Institute of Physics
Bartleby
Fact Index
Furtsch, T.A.
Kang, Nam-Gyu
Wolfram Science World