Thomas Conway <[EMAIL PROTECTED]> wrote in article <[EMAIL PROTECTED]> in gmane.comp.lang.haskell.cafe: > On 8/2/07, apfelmus <[EMAIL PROTECTED]> wrote: > > That concludes the infinite terrain generation for one dimension. For > > higher dimension, one just needs to use 2D objects instead of intervals > > to split into two or more pieces. For instance, one can divide > > equilateral triangles into 4 smaller ones. In fact, it doesn't matter > > whether the starting triangle is equilateral or not when using the > > midpoints of the three sides to split it into four smaller triangles. > Nice.
Nice indeed! The infinite binary tree of the terrain intervals reminds me of the hyperbolic plane, of course, and its use in arbitrary-precision real arithmetic (cue a real mathematician). > The issue of the RNG running backwards was what made me realize > that rather than using StdGen in the nodes, if you simply number them > (Hmmm - the nodes are countably infinite :-)), you can then [e.g.] use > a cryptographic hash or similar to turn them into random numbers. You > can seed the hash to generate different terrains. Isn't the whole point of a good RNG that running it forwards and backwards should be statistically the same? > You may be interested that in some of the code I wrote for the right > angle isosceles triangle case, I got into precision problems. [...] > After pondering on this for a while, I realized instead of > representing the scale of the triangle as a Double, I could use > (Either Double Double), with Left x representing the scale x, and > Right x representing the scale x * sqrt 2 / 2. That way, all the > rounding problems can be made to go away. Well, not all of them - > after all Double has limited digits of mantissa, but down to quite > small scales, the arithmetic will be precise. Actually, you could use > (Either Rational Rational), except that performance would be [even > more] atrocious. What about a possibly infinite list of binary digits in base sqrt(2)? Surely the beauty would overshadow any performance problems. (: -- Edit this signature at http://www.digitas.harvard.edu/cgi-bin/ken/sig "Elegance is optional." -- Richard A. O'Keefe _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
