The Wavelet Transform in the Solution to the Inverse Fractal Problem

The inverse fractal problem for self-affine functions in R^2 is solved by means of testing the invariance of the wavelet transform of the function. The wavelet maxima bifurcation representation used is derived from the continuous wavelet decomposition and possesses translational and scale invariance necessary to reveal the invariance of the self-affine fractal. Algorithms are presented which give satisfactory results for the self-affine fractal and which potentially can be applied to a variety of fractal types in order to solve the related inverse fractal problem.