Dimensional characterization of singular fractal functions

Construction of singular fractal functions which are monotonically increasing functions, differentiable almost everywhere and possess nearly zero derivative, is explained based on an iterative technique of distribution of mass onto a line segment, and their graphs are generated using different values of the two relevant parameters. The fractal dimension of the set of points, called the measureʹs concentrate (where almost the entire mass to be distributed gradually becomes accumulated in successive generations) is found using the result of curdling. The multifractal nature of the measureʹs concentrate, keeping one parameter unchanged and varying another parameter, is pointed out.