| [ KAIST ] in KIDS 글 쓴 이(By): guest (prefrontal) <cortex.stat.wisc> 날 짜 (Date): 2001년 12월 28일 금요일 오전 08시 06분 11초 제 목(Title): Re: [계층구조론]현상과 본질-마치면서 i don't see any 'clear' relationship between fractals and wavelets. A is similar to B in certain aspect does not mean they are equal or has any relationship at all. to show if there are any interesting mathematical relationships, you have to 'clearly' state and prove things. you can say everything to be fractal-like and get away with it. i can even claim that we are god-like and write postings after postings supporting my argument. but then it doesn't prove anything. pure mal-jang-nan. also about linearity and recursive structure, i think chopin has read Godel,Escher & Bach too much. :) you see you have to be very careful about what is linear and what is not linear. it is not simply a single recursive formula that generates nonlinearity but it has something to do with the space where such recursive formula is defined. I will give you one example. let x(n+1)= x(n) +1 and x(0)=0. this is the definition of the natural numbers generated by 'linear' recurrsion. now consider N={1,2,....n}. N can be generated by this 'linear' recurrsion. however there are infinitely many nonlinear recurrsive formulars that can generate this set. think about splines with nodes given by 1,2,...n. in a sense you can make any linear structure nonlinear by restrcting the space where such structure is defined and this is also true for nonlinear system. this is why your favorite 'wavelet expansion' can approximate most functions. :) |