import LSystem

{-##################################################-}
{-# COMPETITION ENTRY: AISTIS STANKEVICIUS 0791918 #-}
{-##################################################-}

{-IMPORTANT: For best view type:   display 1.0 inits                 -}
{-It takes some time to generate the image, so please be patient     -}
{-Also be aware that size of the file is about 40Mbs, sorry for that -}

{-FAKE PIXEL-}
putPixel :: Int -> Int -> Int -> Command
putPixel a x y = GrabPen (p a x y) :#: Go 1 :#: Go (-1)
{-END FAKE PIXEL-}

{-GO TO POSITION X Y-}
gotoXY :: (Int,Int) -> (Int,Int) -> Command
gotoXY (0,0) (x,y) = Go (fromIntegral y) :#: Turn (-90) :#: Go (fromIntegral x) :#: Turn 90
gotoXY (x,y) (0,0) = Go (fromIntegral(-y)) :#: Turn (-90) :#: Go (fromIntegral(-x)) :#: Turn 90
--gotoXY (0,0) (0,0) = Sit

jumpXY (x,y) (x1,y1) = GrabPen Inkless :#: (gotoXY (x,y) (x1,y1))
{-END GO TO POSITION X Y-}

{----MANDELBROT----}
maxIter = 64 {-Number of iterations-}

{-GENERATE AREA-}
area :: [(Int,Int)]
area = [(x,y) | x <- [0..400], y <- [0..400]] {- 400x400 "screen" -}
{-END GENERATE AREA-}

{-EVALUATE PIXELS IN AREA-}
areaEval :: [(Int,(Int,Int))]
areaEval = zip [coordEval (fromIntegral(x),fromIntegral(y)) 0 0 0 0 | (x,y) <- area] area
{-END EVALUATE PIXELS IN AREA-}

{-EVALUATE PIXEL AT XY-}
coordEval :: (Float,Float) -> Int -> Float -> Float -> Float -> Int
coordEval (x,y) i a1 a2 b | (za2(a1,b,x) * za2(a1,b,x) + zb(a1,b,y) * zb(a1,b,y) <= 4) && (i <= maxIter) = coordEval (x,y) (i + 1) (za2(a1,b,x)) (za2(a1,b,x)) (zb(a1,b,y))
			  | (i > maxIter) = 0
			  | (za2(a1,b,x) * za2(a1,b,x) + zb(a1,b,y) * zb(a1,b,y) > 4) = 1

{-Helper functions for computation and adjustment-}
za2 (a1,b,x) = a1*a1 - b*b + c1(x)
zb (a1,b,y) = 2*a1*b + c2(y)
c1 x = x / 400 * 2.8 - 2.2
c2 y = y / 400 * 2.8 - 1.4
{-END EVALUATE PIXEL AT XY-}

{----END MANDELBROT----}

{-INITIATE PLOTTER-}
inits :: Command
inits = adjustPos :#: join[jumpXY (0,0) (x,y) :#: (putPixel n x y) :#: jumpXY (x,y) (0,0) | (n,(x,y)) <- areaEval]
{-END INITIATE PLOTTER-}

{-COLOUR GENERATOR-}
p :: Int -> Int -> Int -> Pen
p a x y | a == 0 = Colour (abs(ca ((y*y*x)`div`(x*x*y)))) 0 (abs(sa (x`div`(y+1))))
	| otherwise = Colour (abs(sa (x`div`(y+1)))) (abs(sa (x`div`(y+1)))) (abs(sa (x`div`(y+1))))

ca a = (cos (fromIntegral(a)))
sa a = (sin (fromIntegral(a)))
{-END COLOUR GENERATOR-}

{-ADJUST STARTING POSITION-}
adjustPos :: Command
adjustPos = GrabPen Inkless :#: Go (-100) :#: Turn 90 :#: Go(300) :#: Turn (-90) 
{-END ADJUST STARTING POSITION-}

{-JOIN LIST OF COMMANDS-}
join :: [Command] -> Command
join a = foldr (:#:) Sit a
{-END JOIN LIST OF COMMANDS-}