Weighted Linear Fractals

Abstract

<p>Linear fractals associated with weights are investigated. Such fractals are important from a conservation law perspective that is relevant in a variety of physical systems such as materials science, sand dune fractals, barred galaxies, as well as in temporal processes like the EEG. Weighted fractals lead to distributions that are consistent with the ubiquitous power law and the first digit phenomenon. Two linear fractal algorithms that are near optimal in the information theoretic sense are described. It is proposed that one mechanism for the emergence of these fractals is the indistinguishability amongst the particles in the evolution and transformation of physical systems.</p>