Shannon entropy, order and image compression

Abstract

The identifcation of nontrivial manifestations of order is of great interest in the field of image analysis. Here, we use image compression as a way to quantify this \order". File compression algorithms (as the ones used in .zip compression) produce smaller files the less disordered the original file is. We apply this principle to various images of dots in disordered dispositions, square lattices and iterations of the Sierpinski carpet, in order to capture a relation between order and image compression. We find that, at least in some cases, we can use compression to quantify order.