/ ray tracer: http://www.nsl.com/k/ray/ray.k

U x is x%sqrt(dot x x)

S r o is if 0>d then inf else if 0>t then inf else if 0<u then u else t
 where (d is sqr(o 1)+sqr b-dot v v)
 where (b is dot v(r 1))
 where (v is (*o)-*r)
 where (t is b+e)
 where (e is sqrt d)
 where u is b-e

I r h o is if ~type(*o) then f(S r(*o)) else g(S r o)
 where (f x is if ~x<*h then h else h(I r)/o 1)
 where g x is if ~x<*h then h else x:,U((*r)-(*o)-x*r 1)

T r h o d l is f(I r h o)
 where (f x is if inf=*x then 0. else g(dot(x 1)l))
 where g y is if ~0>y then 0. else if inf=*I[(*r)+((r 1)**x)+d*x 1;-l]h o then -y else 0.

N n o i is 0 f/+vs 4(!16)
 where f x y is x+T[0 0 -4.;U((i+(y%4)-n%2),n)][inf;3#0.]o(sqrt(2^-42))(U -1 -3 2.)

C k r c is if 1=k then c:r else [c;r*3]:,[c;r]:(C(k-1)(r%2))',+c+(-3 3@vs 2(2 3 6 7))*r%sqrt 12 

R k n is _0.5+15.9375*(N(n*1.)(C k 1.(0 -1 0.)))',+|amend1(vs n(!n*n))0 r where r is |:

F f n v is bwrite f("P5\n",show(n,n),"\n255\n",ci v)

F"c:/temp.pgm"4(R(3)4)