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
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