My parallel of fractals and wavelets that I was expressing, is that both are iterative functions. Hmmm.
My memory of wavelet class is a little fuzzy. Let's see - fractals take the output of the previous calculation and use it as input for the next. Depending on the function chosen, this results in a different result. The coefficients matter but the result will still be similar looking. Thus fractal compression can in theory represent extremely complex things very efficiently if you know what fractal to use.
Wavelets are similar only in that they are also iterative, but if I remember right, the outputs don't feed into each other? The algorithm is more amenable to brute force, a`la Fourier. You can represent almost anything with a chosen function, the question is the efficiency with which it can be done.
Whereas fractals don't work that way. A system of fractals can represent a fern frond for example, but choose a different equation and you may not be able to represent your data at all. A fractal can have a number of complexities also. A fractal can be subtractive, in the form of a Serpinski carpet, or additive, as in a Koch snowflake, to cite two simple examples.
So - I guess my initial thinking was fuzzy and incorrect now that I think about it more.
I remember in class (at SIGGRAPH) skimming over Haar, and going to more complex wavelets that resulted in smoother results more efficiently for 3D surfaces. |
