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To: Kachina who wrote (462)8/9/1999 7:19:00 AM
From: EPS  Read Replies (1) of 626
 
Hi Kachina,

try to do this: make a function equal to 1 on [0,1], zero outside, second step divide [o,1] in two pieces and define a second function to be 1 in [0,1/2], -1 in [1/2,1], and keep repeating the subdivisions. you get an orthonormal system of functions (the *Haar system*).if you try to write functions in terms of series of these Haar functions you need to know the coefficients (just like in Fourier series you need to know the *Fourier coefficients or *Fourier transform*). How many coefficients do you need to get a good approximation of your function/or better how many coefficients do you need so that the error in your approximation is small enough for your needs? compression then means algorithms to select those coefficients efficiently. given the simple nature of the process it is easy to compress and decompress wavelets..note that from one original function (*the mother*) you are able to generate all the other Haar functions. There are of course other more sophisticated *wavelet systems*.

fractals are objects that have *fractional dimension*. sometimes they can be generated by selfsimilarity process associated with a construction similar to the one discussed above. the idea is that each level of resolution you can only see structurally the same that you saw at previous levels. in this fashion complicated worlds can be created with a very simple mechanism. the hope is that sometimes chaotic systems (ie those nonlinear systems where a small perturbation of initial conditions can produce great perturbations) can be described in these terms. of course one can only hope so much but it does happen sometimes..

hopes this helps..

Victor
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