-- Informatics 1 - Functional Programming 
-- William Bradshaw
--
-- To run simply type 'wb' in GHCi


import LSystem

-- Start Command

wb = display (Branch (GrabPen a :#: Go 75 :#: fibcurve6 4 7 a) :#: Turn 180 :#: Branch (GrabPen b2 :#: roots 7) :#: sig)

-- Signature

sig = GrabPen Inkless :#: Turn 50 :#: Go 400 :#: GrabPen black :#: Turn 330 :#:  Go 15 :#: Turn 125 :#: Go 12 :#: Turn 230 :#: Go 12 :#: Turn 125 :#: Go 15 :#: Turn 30 :#: Branch (Go 30) :#: Branch (Turn 180 :#: Go 6):#: Turn 300 :#: Go 10 :#: Turn 290 :#: Go 4 :#: Turn 290 :#: Go 4 :#: Turn 340 :#: negfib 4


-- From Tutorial

split :: Command -> [Command]
split (p :#: q) = (split p)++(split q)
split (Sit) = []
split (x) = [x]

join :: [Command] -> Command
join [] = Sit
join (x:xs) = x :#: join xs

copy :: Int -> Command -> Command
copy x y = join (replicate x y )


--Pens

a, b, c, d, e, f, g, h, i, f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, g1, g2, g3, b1, b2, b3, b4, b5 :: Pen
a = Colour 0.8 0.6 0.0
b = Colour 0.7 0.625 0.0
c = Colour 0.6 0.65 0.0
d = Colour 0.5 0.675 0.0
e = Colour 0.4 0.7 0.0
f = Colour 0.3 0.725 0.0
g = Colour 0.2 0.75 0.0
h = Colour 0.1 0.775 0.0
i = Colour 0.0 0.8 0.0
f1 = Colour 0.3 0.7 0.3
f2 = Colour 0.4 0.5 0.4
f3 = Colour 0.5 0.3 0.5
f4 = Colour 0.6 0.1 0.6
f5 = Colour 0.7 0.0 0.7
f6 = Colour 0.725 0.625 0.225
f7 = Colour 0.75 0.65 0.25
f8 = Colour 0.775 0.675 0.275
f9 = Colour 0.8 0.7 0.30
f10 = Colour 0.825 0.725 0.325
g1 = Colour 0.1 0.7 0.6
g2 = Colour 0.2 0.5 0.8
g3 = Colour 0.3 0.3 1.0
b1 = Colour 0.8 0.6 0.0
b2 = Colour 0.7 0.5 0.0
b3 = Colour 0.7 0.4 0.0 
b4 = Colour 0.7 0.3 0.0 
b5 = Colour 0.7 0.2 0.0

z :: Pen -> Pen
z y | y == a = b
    | y == b = c
    | y == c = d
    | y == d = e
    | y == e = f
    | y == f = g
    | y == g = h
    | y == h = i
    | y == i = f1
    | y == f1 = f2
    | y == f2 = f3
    | y == f3 = f4
    | y == f4 = f5
    | y == f5 = f5
    | y == g1 = g2
    | y == g2 = g3
    | y == g3 = g3
    | y == b1 = b2
    | y == b2 = b3
    | y == b3 = b4
    | y == b4 = b5
    | y == b5 = b5

-- Basics

fib :: Distance  -> Distance
fib 0 = 0
fib 1 = 1
fib x = fib (x-1) + fib (x-2)

curve :: Distance -> Command
curve x = copy 90 (Go (x/pi) :#: Turn 1)

anticurve :: Distance -> Command
anticurve x = copy 90 (Go (x/pi) :#: Turn 359)

-- Original Fibcurves

fibcurve :: Distance -> Command
fibcurve 0 = Sit
fibcurve 1 = curve 1
fibcurve x = curve (fib x) :#: fibcurve (x-1)

antifib :: Distance -> Command
antifib 0 = Sit
antifib 1 = anticurve 1
antifib x = anticurve (fib x) :#: anticurve (x-1)

-- Branching Fibcurve

fibcurve2 :: Distance -> Command
fibcurve2 0 = Sit
fibcurve2 1 = curve 1
fibcurve2 x = (Branch (antifib2 (x-1))) :#: curve (fib x) :#: (fibcurve2 (x-1))

antifib2 :: Distance -> Command
antifib2 0 = Sit
antifib2 1 = anticurve 1
antifib2 x = (Branch (fibcurve2 (x-1))) :#: anticurve (fib x) :#: (antifib2 (x-1))

-- Negative Fibcurve

negfib :: Distance -> Command
negfib 0 = Sit
negfib 1 = curve 1
negfib x = curve (fib x) :#: Turn 180 :#: negfib (x-1)
  
-- Delayed Start Fibcurves

fibcurve3 :: Distance -> Command
fibcurve3 x = curve x :#: fibcurve2 (x-1)

antifib3 :: Distance -> Command
antifib3 x = anticurve x :#: antifib2 (x-1)

-- Coloured Fibcurves

fibcurve4 :: Distance -> Pen -> Command
fibcurve4 0 y = Sit
fibcurve4 1 y = curve 1
fibcurve4 x y = (Branch ((GrabPen (z y) :#: antifib4 (x-1) (z y)))) :#: GrabPen y :#: curve (fib x) :#: GrabPen (z y) :#: (fibcurve4 (x-1) (z y))

antifib4 :: Distance -> Pen -> Command 
antifib4 0 y = Sit
antifib4 1 y = anticurve 1
antifib4 x y = (Branch ((GrabPen (z y) :#: fibcurve4 (x-1) (z y)))) :#: GrabPen y :#: anticurve (fib x) :#: GrabPen (z y) :#: (antifib4 (x-1) (z y))

-- Flowers

fibcurve5 :: Distance -> Distance -> Pen -> Command
fibcurve5 q 0 y = Sit
fibcurve5 q 1 y = star2 8 (q-2) f2
fibcurve5 q x y = (Branch ((GrabPen (z y) :#: antifib5 q (x-1) (z y)))) :#: GrabPen y :#: curve (fib x) :#: GrabPen (z y) :#: (fibcurve6 q (x-1) (z y))

antifib5 :: Distance -> Distance -> Pen -> Command
antifib5 q 0 y = Sit
antifib5 q 1 y = anticurve 1
antifib5 q x y = (Branch ((GrabPen (z y) :#: fibcurve6 q (x-1) (z y)))) :#: GrabPen y :#: anticurve (fib x) :#: GrabPen (z y) :#: (antifib6 q (x-1) (z y))

fibcurve6 :: Distance -> Distance -> Pen -> Command
fibcurve6 q 0 y = Sit
fibcurve6 q 1 y = star2 8 (q-2) g1
fibcurve6 q x y = (Branch ((GrabPen (z y) :#: antifib5 q (x-1) (z y)))) :#: GrabPen y :#: curve (fib x) :#: GrabPen (z y) :#: (fibcurve5 q (x-1) (z y))

antifib6 :: Distance -> Distance -> Pen -> Command
antifib6 q 0 y = Sit
antifib6 q 1 y = anticurve 1
antifib6 q x y = (Branch ((GrabPen (z y) :#: fibcurve5 q (x-1) (z y)))) :#: GrabPen y :#: anticurve (fib x) :#: GrabPen (z y) :#: (antifib5 q (x-1) (z y))

-- Stars

star :: Distance -> Command
star x = Branch (fibcurve4 x a) :#: Turn 90 :#: Branch (fibcurve4 x a) :#: Turn 90 :#: Branch (fibcurve4 x a):#: Turn 90 :#: fibcurve4 x a

star2 :: Int -> Distance -> Pen -> Command
star2 z 0 y = Sit
star2 z 1 y = Sit
star2 z x y = copy z (Branch (fibcurve6 x x y) :#: Turn (360/(fromIntegral z)))

-- Roots

roots :: Int -> Command
roots 0 = Sit
roots x = Branch (p :#: Go 50 :#: roots (x-1)) :#: Branch (q :#: Go 50 :#: roots (x-1))
          where
            p = Turn (15)
            q = Turn (345)