Brownian motion of sol particles under ultramicroscopes and for bigger particles even under ordinary microscopes. The Brownian motion becomes progressively less prominent, as the particles grow in size or the viscosity of the medium increases. Brownian motion of sol particles Colloidal particles in a sol are continuously bombarded by the molecules of the dispersion medium on all sides. The impacts are however not equal in every direction. As a result, the sol particles show random or zig-zag movements. This random or zig-zag motion of the colloidal particles in a sol is called Brownian motion or Brownian movement. The phenomenon of Brownian motion was observed by
Fractional Brownian motion to a smoother motion. It was introduced by . The value of "H" determines what kind of process the "fBm" is: The increment process, "X"("t") = "B"("t"+1) − "B"("t"), is known as fractional Gaussian noise. There is also a generalization of fractional Brownian motion: "n"-th order fractional Brownian motion, abbreviated as n-fBm. n-fBm is a Gaussian, self-similar, non-stationary process whose increments of order "n" are stationary. For "n" = 1, n-fBm is classical fBm. Like the Brownian motion that it generalizes, fractional Brownian motion is named after 19th century biologist Robert Brown; fractional Gaussian noise is named after mathematician Carl