In mathematics, self-affinity is a feature of a fractal whose pieces are scaled by different amounts in the x- and y-directions. This means that to appreciate the self similarity of these fractal objects, they have to be rescaled using an anisotropic affine transformation.

self-affinity is a linear transformation which gives periodic figure.

Wiener's scalar Brownian motion B(t) is the process starting with B(0) = 0 and having the following property:

for every collection of non-overlapping intervals Δt, the increments of B(t) are independent and stationary Gaussian variables B(t) has the following well-known invariance property:

The random processes B(t) and b^(− 1/2) B(bt) are identical in distribution for every ratio b > 0.

Since the rescaling ratios of t and of B are different, the transformation from B(t) to b^(− 1/2) B(bt) is an affinity.