An L^2-function on a finite volume hyperbolic surface is called non-autocorrelated if it is perpendicular to its image under A_r, the operator of averaging over the circle of radius r, where r is fixed. We show that the support of such a function is small, namely, it takes not more than (r+1) / exp(r/2) of the volume of the surface. In my talk, I'll prove this result, and show its connection to the equidistribution of the circle on a surface (proved by Nevo). As a corollary, this bound implies that the chromatic number of a surface with respect to the forbidden distance r grows exponentially with r.