Fractals and multifractals in early-stage spinodal decomposition and continuous ordering

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Abstract
Systems undergoing spinodal decomposition often exhibit an interconnected morphology similar to a fractal in the early stage. It has been speculated that this early-stage structure is in fact a fractal. In this Letter I show that the linear theory of spinodal decomposition does indeed predict that the early-stage morphology is fractal and, in addition, has what one might call a multifractal structure. In contrast, there is no fractal or multifractal structure in continuous ordering. In addition, I construct percolation cluster growth models isomorphic to spinodal decomposition and continuous ordering so that precise tests of these predictions can be performed.