Hi Marc,
Thanks for the link.
A jaw dropping photo and an all-round wonderful web site.
I happened across this page where they discuss "Quantifying Crater Shapes" :-
http://lroc.sese.asu.edu/posts/864
Quote:
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Originally Posted by LROC
Among many polynomials, we found the Chebyshev polynomials to be particularly suited to successfully describe crater shapes.
Chebyshev Coefficients
We found that the topography of nearly all lunar craters can be represented by a relatively small set of the Chebyshev polynomials (a subset is shown below). In this representation, the individual polynomial functions are scaled and summed to approximate the actual crater elevation profile. The scaling factors are the Chebyshev coefficients.
The individual Chebyshev functions each represent a component of the overall crater shape (such as, part of the crater rim, wall, or floor) and, combined with the corresponding coefficients, describes a particular crater. Thus only the coefficients change from crater to crater, allowing the creation of a vast and highly precise database of lunar crater shapes!
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It reminded me of the character
Slartibartfast in Douglas Adams "The Hitchhiker's Guide to the Galaxy".
Slartibartbast is a designer of planets and he is working on the design
for the coastline of Africa for a new Earth after the original was destroyed.
Quote:
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Originally Posted by Slartibartfast
"In this replacement Earth we're building they've given me Africa
to do and of course I'm doing it with all fjords again because I
happen to like them, and I'm old fashioned enough to think that
they give a lovely baroque feel to a continent.
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Slartibartfast would probably reach for fractals rather than polynomials.