From: Bill Gosper <gosper@alum.mit.edu>
Due to a 2D pattern-generator discovered by two exceptional brothers I'm tutoring: http://gosper.org/p5d1.png .
Notice the pentagrams are a little bit skewed. A program I wrote also generates skewed pentagonal patterns in a square grid when run with certain settings:
http://www.tiac.net/~sw/2005/03/Mandala/minsky10.html
From: Fred lunnon <fred.lunnon@gmail.com>
This might make an interesting wall design for a public space ...
As long as certain members of the public don't know you did it.
Any comments on how it's done? WFL
Mine is, find cycles in a function that rotates a grid by 36 degrees, but using a cheat method by Minsky: http://www.inwap.com/pdp10/hbaker/hakmem/hacks.html#item149 and illuminated by, er, Gosper: http://www.inwap.com/pdp10/hbaker/hakmem/hacks.html#item151
It's something like epsilon = sqrt( 2 * ( 1 - cos( pi / 10 ) ) ); x = x - round( epsilon * y ); // old y y = y + round( epsilon * x ); // new x
This page explains my program in more detail & has an applet to play with: http://www.tiac.net/~sw/2005/03/Mandala/
--Steve
Yow, that substantially intersects what they're doing as they aggressively investigate Minsky's algorithm. It looks like you'll have to coauthor their Intelligencer paper! But they have found more knobs to turn. And almost every time we turn one, we get eye candy. http://gosper.org/p12d23.png, http://gosper.org/p2pid1.png . --rwg