As I understand we can perform a Fourier transform (2 dimensional ) on a class of matrix and get Fourier coefficients; and from those coefficients we can get back the original matrix. In other words Fourier coefficients forms a one to one map with the original matrix. Not sure I am expressing my self correctly mathematically but I hope it is understood. The question is if such bases exist in fractal domain? The wikipedia link of fractal is :
https://en.wikipedia.org/wiki/Fractal
I can understand the kind of matrix for which the fractal bases exist may be very limited and Fourier bases exist for much broader class of matrix. I am interested to know what kind of matrix has the fractal kind of basis? Mostly can we transform a matrix so that it has a fractal bases?