We study fractal measures on Euclidean space through the dynamics of “zooming in” on typical points. The resulting family of measures (the “scenery”), can be interpreted as an orbit in an appropriate dynamical system which often equidistributes for some invariant distribution. The first part of the paper develops basic properties of these limiting distributions and the relations between them and other models of dynamics on fractals, specifically to Zähle distributions and Furstenberg’s CP… CONTINUE READING