Fractal landscape dynamics in dense emulsions and stock prices

Many soft and biological materials display so-called 'soft glassy' dynamics; their constituents undergo anomalous random motion and intermittent cooperative rearrangements. Stock prices show qualitatively similar dynamics, whose origins also remain poorly understood. Recent simulations of a foam have revealed that such motion is due to the system evolving in a high-dimensional configuration space via energy minimization on a slowly changing, fractal energy landscape. Here we show that the salient geometrical features of such energy landscapes can be explored and quantified not only in simulation but empirically using real-world, high-dimensional data. In a mayonnaise-like dense emulsion, the experimentally observed motion of oil droplets shows that the fractal geometry of the configuration space paths and energy landscape gives rise to the anomalous random motion and cooperative rearrangements, confirming corresponding simulations in detail. Our empirical approach allows the same analyses to be applied to the component stock prices of the Standard and Poor's 500 Index. This analysis yields remarkably similar results, revealing that stock return dynamics also appear due to prices moving on a similar, slowly evolving, high-dimensional fractal landscape.