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# tlehman/mandelbrot.hs Secret

Created June 12, 2024 01:00
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 -- mandelbrot.hs using recursion and lazy infinite lists module Mandelbrot where import Data.Complex -- x :+ y is how the complex number x + iy is represented in Haskell -- a point c ∈ ℂ is in the Mandelbrot set if |z_n| ≤ 2 for all n>0 -- z_n = z_{n-1}^2 + c -- this is how the values expand: ((z**2 + c)**2 + c)**2 + c -- it looks like: -- foldl (\z c -> \z**2 + c) 0 [c,c,c...] -- -- repeat :: a -> [a] -- repeat c -- => [c,c,c....] -- -- (zn n c) returns the value z_n, where z_n = z_{n-1}^2 + c zn :: RealFloat a => Int -> Complex a -> [Complex a] zn n c = take n \$ iterate (\z -> z**2 + c) 0 inMandelbrotSet :: (RealFloat a, Ord a) => Complex a -> Bool inMandelbrotSet c = (realPart . abs \$ last \$ zn 1000 c) < 2 -- showBool is for displaying a True value as a * and a False value as a " " for use in print showBool :: Bool -> Char showBool b = if b then '*' else ' ' -- split a list into chunks of a given size chunk :: Int -> [a] -> [[a]] chunk _ [] = [] chunk n xs = let (ys, zs) = splitAt n xs in ys : chunk n zs chunkSize = 20 color = (showBool . inMandelbrotSet) grid = chunk chunkSize [color (re :+ im) | re <- take chunkSize [-1.0,-0.9..], im <- take chunkSize [-1.0,-0.9..]] main :: IO () main = do putStrLn (concat (map (\l -> l ++ "\n") grid))

### tlehman commented Jun 12, 2024

``````λ> main
*****
*****
***
*****
*********
*************
***********
*************
*****************
*****************
*************
*************
***********
***** *****
``````