Hello! I'm developing a program that (among other things) will
be implementing the algorithm on page 108 of "Science of Fractal
Images" by Peitgen and Saupe. It's working fine; but I've come
across something I don't understand. On pages 106 and 107 are
a sequence of spectrally synthesized mountains. On page 109:
"In the sequence...we show how the spectral synthesis method
'adds detail' by improving the spectral representation of the
random fractal, i.e. by allowing more and more Fourier coefficients
to be employed. The resolution...was N=64 but in the top image...
only the first 4 coefficients were used. In the other pictures we
allowed 16 and 64 non-zero coefficients..."
Now, here's my problem. I'm not sure _where_ to pick the "first
M coefficients.", and how to pass that information to the Fourier
transform. Obviously, some of the coefficients need to be zeroed
out, but which ones? The key to making it work right is satisfying
the conjugate symmetry condition mentioned on page 109, but I'm
still at a loss figuring out which are the "first" ones. It is not
just the first M ones calculated; the algorithm as presented does
a fairly optimal job of calculating the things. (Though there are
some redundant calculations.)
Could anyone help me with this? Fast? Help?
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