ERROR-BOUNDS ON THE ESTIMATION OF FRACTAL DIMENSION

The use of fractal dimension as an index of complexity is widely used in natural science. Studies related to the significance of the estimat es obtained have rarely been presented in the past. This paper is inte nded to present an error analysis in the estimation of the fractal dim ension of a particular class of objects, namely, graphs of Knopp funct ions. The algorithm used to estimate the fractal dimension is the vari ation method. Various numerical approximations of the variation will b e presented. Using functional properties of the chosen parametric fami ly of sets, we derive error bounds useful in the assessment of the acc uracy that can be achieved in the numerical approximation of the dimen sion at a given scale and resolution.