Multifractal and chaos of one dimensional maps

We present an accurate method to find the period doubling solutions of general one dimensional iterative maps. Due to the asymmetry of the bifurcation graph, period doubling factors defining the asymmetry are introduced. This additional information on the asymmetry give more accurate results than using just the usual multifractal analysis alone. Multiple period doubling leading to chaos is only straight forward extension. The fractal characteristic parameters can be calculated with high precision by means of the Feigenbaum numbers. The limiting system parameter which leads to chaos is obtained analytically by equating the two parameters at consecutive period doublings.