Methods suggested in the past for simulated ore concentration or pollution concentration over an area of interest, subject to the condition that the simulated surface is passing through specifying points, are based on the assumption of normality. A new method is based on the construction of a fractal plane-to-line function f(x,y,R,e,u), where (x,y) is in (a,b) X (c,d), R is the autocorrelation function, e is the resolution limit, and u is a random real function on (-1,1). The simulation using fractals escapes from any distribution assumptions of the data. The given network of points is connected to form quadrilaterals; each one of the quadrilaterals is split based on ways which are extensions of the well-known subdivision method. The quadrilaterals continue to split and grow until resolution obtained in both x and y directions is smaller than a prespecified resolution. (Copyright (c) 1988 International Association for Mathematical Geology.)