Michael Feathers mfeathers at mindspring.com
Sun Jul 6 21:02:14 EDT 2008

```Decided a while ago to write some code to calculate the Mandelbrot set
using the escape iterations algorithm.  Discovered after mulling it
about that I could just built it as an infinite list of infinite lists
and then extract any rectangle of values that I wanted:

type Point = (Double, Double)

sq :: Double -> Double
sq x = x ^ 2

translate :: Point -> Point -> Point
translate (r0, i0) (r1, i1) =
(r0 + r1, i0 + i1)

mandel :: Point -> Point
mandel (r, i) =
(sq r + sq i, 2 * r * i)

notEscaped :: Point -> Bool
notEscaped (r, i) =
(sq r + sq i) <= 4.0

trajectory :: (Point -> Point) -> [Point]
trajectory pointFunction =
takeWhile notEscaped \$ iterate pointFunction seed
where seed = (0.0, 0.0)

escapeIterations :: (Point -> Point) -> Int
escapeIterations =
length . tail . take 1024 . trajectory

mandelbrot :: Double -> [[Int]]
mandelbrot incrementSize =
[[ escapeIterations \$ translate (x, y) . mandel
| x <- increments]
| y <- increments] where
increments = [0.0, incrementSize .. ]

window :: (Int, Int) -> (Int, Int) -> [[a]] -> [[a]]
window (x0, y0) (x1, y1) = range x0 x1 . map (range y0 y1) where
range m n = take (n - m) . drop m

```