Given two coordinates, compute the Ulam spiral number at that place.

Ulam.hs

import Data.Char

ch = chr . (+65)

-- east quadrant
ulam x y | x > y && x > -y   = (x*2 - 1)^2 + (x + y) - 1

-- north quadrant
ulam x y | x <= y && x > -y  = (y*2)^2 - (x + y)

-- west quadrant
ulam x y | x <= y && x <= -y = (x*2)^2 - (x + y)

-- south quadrant (default)
ulam x y                     = (y*2 - 1)^2 + (x + y) - 1


matrix = [[ch $ ulam x y | x <- [-4 .. 4]] | y <- reverse [-4 .. 4]]

vis = mapM_ putStrLn matrix


primes = [2,3] ++ filter isPrime [5,7 ..]

isPrime x = and [x `rem` p /= 0 | p <- takeWhile (\p -> p*p <= x) primes]

pmatrix :: Int -> [String]
pmatrix w = [[test $ ulam x y | x <- [-w .. w]] | y <- reverse [-w .. w]]
   where test n = ch $ isPrime (n + 2)
         ch True = '@'
         ch _ = ' '

prvis w = mapM_ putStrLn (pmatrix w)