-- Put your name and matriculation number here -- Hugh Cole-Baker 0568731 --My entry into the programming competition is at the end of this file, --after question 10. To display it enter "display 2.0 sunflowers" at the --prompt. import LSystem import Numeric -- 1. The test for the empty list here is so that the function can be used --in question 7 without introducing a Sit into the command. Otherwise I use --foldl1 as it doesn't require any unit value. join :: [Command] -> Command join xs | xs == [] = Sit | otherwise = foldl1 (:#) xs -- 2. When using (xs :# x) to match a number of Commands, all but the last --Command is assigned to xs and the last Command is assigned to x. This --means that the recursion in this definition works the other way around --from normal recursive definitions i.e. it starts with the last item. split :: Command -> [Command] split Sit = [Sit] split (Go d) = [Go d] split (Turn a) = [Turn a] split (xs :# x) = (split xs) ++ [x] -- 3. This just replicates the Command n times and joins the list of replicated --Commands together copy :: Int -> Command -> Command copy n c = join (replicate n c) -- 4. Draws a hexagon by repeating Go d :# Turn 60 6 times hexagon :: Distance -> Command hexagon d = copy 6 (Go d :# Turn 60) -- 5. The same idea as question 4, but adapted for regular polygons of any --number of sides. It works out the external angle by dividing 360 by n. polygon :: Distance -> Int -> Command polygon d n = copy n (Go d :# Turn (360 / fromIntegral n)) -- 6. Draws a spiral made out of short lines. dm is the starting line --length, n is the number of segments, ds is the amount to decrease the --line length by every segment, and a is the angle to turn after each segment. spiral :: Distance -> Int -> Distance -> Angle -> Command spiral _ 0 _ _ = Sit spiral dm n ds a = Go dm :# Turn a :# (spiral (dm - ds) (n - 1) ds a) -- 7.The optimise function works in two passes, firstly to remove any single --Command which has no function, then to join together any adjacent Turn or Go --Commands (as long as this isn't going to result in another Go 0 or Turn 0) --The first and second functions work on lists of Commands as it's --easier to do recursion on lists. The lists are joined into a single Command --at the end. optimiseFirst :: [Command] -> [Command] optimiseFirst cs = [c | c <- cs , c /= Sit , c /= (Go 0) , c /= (Turn 0)] optimiseSecond :: [Command] -> [Command] optimiseSecond [] = [] optimiseSecond ((Go a):(Go b):cs) = if (a + b) == 0 then optimiseSecond cs else optimiseSecond ((Go (a + b)):cs) optimiseSecond ((Turn a):(Turn b):cs) = if (a + b) == 0 then optimiseSecond cs else optimiseSecond ((Turn (a + b)):cs) optimiseSecond (c:cs) = c:(optimiseSecond cs) optimise :: Command -> Command optimise c = join (optimiseSecond (optimiseFirst (split c))) -- 8. Implements the arrowhead L-System arrowhead :: Int -> Command arrowhead x = f x where f 0 = GrabPen red :# Go 10 f (x+1) = g x :# p :# f x :# p :# g x g 0 = GrabPen green :# Go 10 g (x+1) = f x :# n :# g x :# n :# f x n = Turn 60 p = Turn (-60) -- 9. Implements the branch L-System branch :: Int -> Command branch x = g x where g 0 = GrabPen red :# Go 10 g (x+1) = f x :# n :# Branch (Branch (g x) :# p :# g x) :# p :# f x :# Branch (p :# f x :# g x) :# n :# g x f 0 = GrabPen green :# Go 10 f (x+1) = f x :# f x n = Turn 22.5 p = Turn (-22.5) -- 10. Implements the Hilbert L-System hilbert :: Int -> Command hilbert x = l x where f = GrabPen blue :# Go 10 l 0 = GrabPen green :# Go 10 l (x+1) = p :# r x :# f :# n :# l x :# f :# l x :# n :# f :# r x :# p r 0 = GrabPen red :# Go 10 r (x+1) = n :# l x :# f :# p :# r x :# f :# r x :# p :# f :# l x :# n n = Turn 90 p = Turn (-90) --The following is my entry into the 2005 Informatics Programming Competition. --It consists of a bitmap picture encoded as a string, --a palette to draw the picture with, and functions to generate a Command that --draws the bitmap using turtle graphics. 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The values of --the three characters correspond to colours in the palette. picture :: [String] picture = [". + @ # $ % & * = - ; > , ' ) ! ~ { { ] ^ / ( _ : < [ [ } | 1 2 3 4 5 6 7 8 9 0 a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ` . .. +. @. #. $. v %. &. *. =. -. ;. >. ,. '. ). ", "!. ~. {. ]. ^. /. (. _. :. <. [. }. |. 1. 2. 3. 4. 1. 5. 6. 7. 8. 9. 0. a. b. c. d. e. f. g. h. i. j. k. l. m. n. o. p. q. r. s. t. u. v. w. x. y. z. A. B. C. D. E. F. G. H. I. J. K. L. M. N. O. P. Q. F. R. S. T. U. V. W. X. Y. Z. `. + .+ ++ @+ #+ $+ %+ &+ *+ =+ -+ ;+ >+ ,+ '+ )+ !+ ~+ {+ ]+ ^+ /+ (+ _+ :+ <+ [+ }+ |+ 1+ 2+ 3+ ", "4+ 5+ 6+ 7+ 8+ 9+ 0+ a+ (. b+ c+ d+ e+ f+ g+ h+ f+ i+ j+ k+ l+ m+ n+ o+ p+ q+ r+ s+ t+ u+ v+ w+ x+ y+ z+ A+ B+ C+ D+ E+ F+ G+ H+ I+ J+ K+ w+ L+ M+ N+ O+ P+ Q+ R+ S+ T+ U+ V+ W+ X+ Y+ Z+ `+ @ .@ +@ @@ #@ $@ %@ &@ *@ =@ -@ ;@ >@ ,@ '@ )@ !@ ~@ {@ ]@ ^@ /@ (@ _@ :@ <@ [@ }@ |@ 1@ 2@ 3@ 4@ 5@ 6@ 7@ 8@ 9@ 0@ a@ b@ c@ d@ e@ f@ g@ h@ ", "i@ j@ k@ l@ m@ n@ o@ p@ q@ r@ s@ t@ u@ v@ w@ u@ x@ y@ z@ A@ B@ C@ D@ E@ D. F@ G@ H@ I@ J@ K@ L@ M@ N@ O@ P@ Q@ R@ S@ T@ U@ V@ W@ X@ Y@ Z@ `@ # .# +# @# ## $# %# &# *# =# -# ;# ># ,# '# )# !# ~# {# ]# ^# /# (# _# :# <# [# }# |# 1# 2# 3# 4# 5# 6# 7# 8# 9# 0# a# b# c# d# e# f# g# h# i# j# k# l# m# E. n# o# g# p# q# r# s# t# u# v# ", "w# x# y# z# A# B# C# D# E# F# D. 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[(String,Pen)] -> Pen lookupColour str pal = (head [b | (a,b) <- pal, str == a]) --This converts one line of the picture to a Command which draws that line lineToCommand :: String -> Command lineToCommand [] = Sit lineToCommand (a:b:c:xs) = (GrabPen (lookupColour (a:b:[c]) (paletteToPairs palette))) :# (Go pixelWidth) :# lineToCommand xs --This uses lineToCommand to convert an entire picture to a Command pictureToCommand :: [String] -> Command pictureToCommand [] = Sit pictureToCommand (x:xs) = (lineToCommand x) :# GrabPen Inkless :# Turn (-90) :# (Go lineSpacing) :# Turn (-90) :# Go (pixelWidth * width) :# Turn 90 :# (Go lineSpacing) :# Turn 90 :# pictureToCommand xs --The final result, the initial Turn (-90) is needed so the picture is drawn --the right way around sunflowers :: Command sunflowers = Turn (-90) :# (pictureToCommand picture)

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