Cabal init in the folder

Author: gauravnv

AnimV1.gif

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+Copyright (c) 2019 RNG
+
+Permission is hereby granted, free of charge, to any person obtaining
+a copy of this software and associated documentation files (the
+"Software"), to deal in the Software without restriction, including
+without limitation the rights to use, copy, modify, merge, publish,
+distribute, sublicense, and/or sell copies of the Software, and to
+permit persons to whom the Software is furnished to do so, subject to
+the following conditions:
+
+The above copyright notice and this permission notice shall be included
+in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
+CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
+TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
+SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

AnimV2.gif

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+import Distribution.Simple
+main = defaultMain

ChangeLog.md

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+-- Initial haskell-av-mandelbrot.cabal generated by cabal init.  For 
+-- further documentation, see http://haskell.org/cabal/users-guide/
+
+-- The name of the package.
+name:                haskell-av-mandelbrot
+
+-- The package version.  See the Haskell package versioning policy (PVP) 
+-- for standards guiding when and how versions should be incremented.
+-- https://wiki.haskell.org/Package_versioning_policy
+-- PVP summary:      +-+------- breaking API changes
+--                   | | +----- non-breaking API additions
+--                   | | | +--- code changes with no API change
+version:             0.1.0.0
+
+-- A short (one-line) description of the package.
+-- synopsis:            
+
+-- A longer description of the package.
+-- description:         
+
+-- URL for the project homepage or repository.
+homepage:            https://github.com/gauravnv/haskell-av-mandelbrot
+
+-- The license under which the package is released.
+license:             MIT
+
+-- The file containing the license text.
+license-file:        LICENSE
+
+-- The package author(s).
+author:              RNG
+
+-- An email address to which users can send suggestions, bug reports, and 
+-- patches.
+-- maintainer:          
+
+-- A copyright notice.
+-- copyright:           
+
+category:            Graphics
+
+build-type:          Simple
+
+-- Extra files to be distributed with the package, such as examples or a 
+-- README.
+extra-source-files:  ChangeLog.md, README.md
+
+-- Constraint on the version of Cabal needed to build this package.
+cabal-version:       >=1.10
+
+
+executable haskell-av-mandelbrot
+  -- .hs or .lhs file containing the Main module.
+  main-is:             Main.hs
+  
+  -- Modules included in this executable, other than Main.
+  -- other-modules:       
+  
+  -- LANGUAGE extensions used by modules in this package.
+  -- other-extensions:    
+  
+  -- Other library packages from which modules are imported.
+  build-depends:       base >=4.9 && <4.10
+  
+  -- Directories containing source files.
+  hs-source-dirs:      src
+  
+  -- Base language which the package is written in.
+  default-language:    Haskell2010
+  

LICENSE

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-import Codec.Picture
-import Codec.Picture.Types
-import System.Environment
--- import Codec.FFmpeg
-
-main :: IO ()
-main = do
-    putStrLn "Beginning rendering of image."
-    makenframes 1 100
-
-makenframes :: Int -> Int -> IO ()
-makenframes n end
- 							| n >= end = putStrLn "Completed all"
-							| otherwise    = do
-																savePngImage ("frames\\"++(show n)++".jpg") (generateFractal n)
-																putStrLn ("Completed"++(show n))
-																makenframes (n+1) end
-offset :: (Float, Float)
-offset = (0.099, 0.89398)
-
-zoomfactor :: Float
-zoomfactor = 0.03
-
-width :: Int
-width = 400
-
-height :: Int
-height = 300
-
-generateFractal :: Int -> DynamicImage
-generateFractal n = ImageRGB8 $ (generateImage (mandelbrot n)) width height
-
-iters :: Int -> Int
-iters n = 25 + n*n
-
-palette :: Int -> [PixelRGB8]
-palette n = foldr (\a -> \b -> (PixelRGB8 (fromIntegral a*10) (fromIntegral a*5) (fromIntegral a*2)):b) [] [0..(iters n)]
-
-mandelbrot :: Int -> Int -> Int -> PixelRGB8
-mandelbrot n x0 y0 = getColor 0 0 0 n
-    where getColor :: Float -> Float -> Int -> Int -> PixelRGB8
-          getColor x y i n = if x*x + y*y < 2*2 && i < (iters n)
-                           then getColor (x*x - y*y + (scaleX x0 n)) (2*x*y + (scaleY y0 n)) (i+1) n
-                           else (palette n)!!i
-
-scaleX :: Int -> Int -> Float
-scaleX x n = (3.5/ (zoomfactor*(fromIntegral (n*n*n)))) * (fromIntegral x) / (fromIntegral width) - fst offset-- - zoomfactor * (fromIntegral n))
-
-scaleY :: Int -> Int -> Float
-scaleY y n = (2/ (zoomfactor*(fromIntegral (n*n*n)))) * (fromIntegral y) / (fromIntegral height) - snd offset-- - zoomfactor * (fromIntegral n))
+import Codec.Picture
+import Codec.Picture.Types
+import System.Environment
+-- import Codec.FFmpeg
+
+main :: IO ()
+main = do
+    putStrLn "Beginning rendering of image."
+    makenframes 1 100
+
+makenframes :: Int -> Int -> IO ()
+makenframes n end
+ 							| n >= end = putStrLn "Completed all"
+							| otherwise    = do
+																savePngImage ("frames\\"++(show n)++".jpg") (generateFractal n)
+																putStrLn ("Completed"++(show n))
+																makenframes (n+1) end
+offset :: (Float, Float)
+offset = (0.099, 0.89398)
+
+zoomfactor :: Float
+zoomfactor = 0.03
+
+width :: Int
+width = 400
+
+height :: Int
+height = 300
+
+generateFractal :: Int -> DynamicImage
+generateFractal n = ImageRGB8 $ (generateImage (mandelbrot n)) width height
+
+iters :: Int -> Int
+iters n = 25 + n*n
+
+palette :: Int -> [PixelRGB8]
+palette n = foldr (\a -> \b -> (PixelRGB8 (fromIntegral a*10) (fromIntegral a*5) (fromIntegral a*2)):b) [] [0..(iters n)]
+
+mandelbrot :: Int -> Int -> Int -> PixelRGB8
+mandelbrot n x0 y0 = getColor 0 0 0 n
+    where getColor :: Float -> Float -> Int -> Int -> PixelRGB8
+          getColor x y i n = if x*x + y*y < 2*2 && i < (iters n)
+                           then getColor (x*x - y*y + (scaleX x0 n)) (2*x*y + (scaleY y0 n)) (i+1) n
+                           else (palette n)!!i
+
+scaleX :: Int -> Int -> Float
+scaleX x n = (3.5/ (zoomfactor*(fromIntegral (n*n*n)))) * (fromIntegral x) / (fromIntegral width) - fst offset-- - zoomfactor * (fromIntegral n))
+
+scaleY :: Int -> Int -> Float
+scaleY y n = (2/ (zoomfactor*(fromIntegral (n*n*n)))) * (fromIntegral y) / (fromIntegral height) - snd offset-- - zoomfactor * (fromIntegral n))

README.md

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+import Data.Complex
+import Data.Maybe (listToMaybe, isNothing, maybe, catMaybes)
+import Control.Monad
+import Control.Applicative ((<$>))
+import System.Environment (getArgs)
+import System.Console.GetOpt
+import Control.Arrow ((***), second)
+
+type Point = Complex Double
+type Image c = Point -> c
+type Fractal c = Int -> Image c -- | given an iteration count, generates an image
+
+fractal ::     (Point -> (a -> a))  -- | iterated function
+            -> (a -> Maybe c)       -- | convergence criterion
+            -> (Point -> a)         -- | iteration start            
+            -> Int                  -- | iteration limit
+            -> Image (Maybe (Int, c))
+fractal f cc sf l p = listToMaybe . catMaybes .  zipWith ((<$>) . (,)) [0..l] . map cc . iterate (f p) . sf $ p
+
+newton ::      (Point -> Point)     -- | the function
+            -> (Point -> Point)     -- | its derivative
+            -> Fractal (Maybe (Int, Point))
+newton f f' = fractal (const next)
+                    (\z -> if next z == z then Just z else Nothing)
+                    id
+    where
+        next z = z - f z/f' z
+
+mandelbrot :: Fractal (Maybe (Int, ()))
+mandelbrot = fractal (\c z -> z*z + c)
+                    (\z -> if magnitude z > 2 then Just () else Nothing)
+                    (const 0)
+
+julia :: Point -> Fractal (Maybe (Int, ()))
+julia p = fractal (\c z -> z*z + p)
+                  (\z -> if magnitude z > 2 then Just () else Nothing)
+                  id
+
+convergence :: Image (Maybe (Int, a)) -> Image Int
+convergence = fmap (maybe 0 ((+1) . fst))
+
+writePgm :: Image Int -> Point -> Point -> Double -> IO ()
+writePgm f ll ur scale =
+    do
+        putStrLn "P5"
+        print width 
+        print height 
+        putStrLn "255"
+        forM_ [0.. height-1] $ \i -> let y = fromIntegral i/scale in
+            forM_ [0.. width-1] $ \j -> let x = fromIntegral j/scale in
+                let z = (x :+ y) + ll in (putChar . toEnum . f $ z)
+    where
+        width = floor $ scale * realPart (ur-ll)
+        height = floor $ scale * imagPart (ur-ll)
+
+fractSpec :: FractSpec -> Fractal Int
+fractSpec Mandelbrot = convergence . mandelbrot
+fractSpec (Julia p) = convergence . julia p
+fractSpec (Newton roots) = convergence . newton f f'
+    where 
+        f z = product $ map (z-) roots
+        f' z = let factors = map (z-) roots
+                in sum . map product . dropEach $ factors
+        dropEach [] = []
+        dropEach (x:xs) = xs:map (x:) (dropEach xs)
+
+data FractSpec = Newton [Point] | Mandelbrot | Julia Point
+data Options = Options
+                { optScale :: Double
+                , optBotLeft :: Complex Double
+                , optTopRight :: Complex Double
+                , optType :: FractSpec
+                }
+
+defaultOptions = Options
+                    { optScale=100.0
+                    , optBotLeft=negate (1 :+ 1)
+                    , optTopRight=(1 :+ 1)
+                    , optType=Mandelbrot
+                    }
+
+options :: [OptDescr (Options -> Options)]
+options = [ Option ['s'] ["scale"] (ReqArg (\x opt -> opt { optScale=read x } ) "SCALE")
+                "scale 1 unit to SCALE pixels"
+          , Option [] ["ll", "lower-left"] (ReqArg (\x opt -> opt { optBotLeft=readC x } ) "X,Y")
+                "set lower left of viewport to X,Y"
+          , Option [] ["ur", "upper-right"] (ReqArg (\x opt -> opt { optTopRight=readC x } ) "X,Y")
+                "set upper right of viewport to X,Y"
+          , Option ['m'] ["mandelbrot"] (NoArg (\opt -> opt { optType=Mandelbrot } ))
+                "render the Mandelbrot set"
+          , Option ['j'] ["julia"] (ReqArg (\x opt -> opt { optType=Julia (readC x) } ) "X,Y")
+                "render the Julia set at X,Y"
+          , Option ['n'] ["newton"] (ReqArg (\x opt -> opt { optType=Newton (readCs x) } ) "X1,Y1:X2,Y2:...")
+                "render the Newton fractal for a polynomial with roots at X1,Y1, X2,Y2, ..."
+        ]
+    where
+        readC :: String -> Complex Double
+        readC = uncurry (:+) . (read *** (read . tail)) . span (/= ',')
+        readCs = map readC . split
+
+        split :: String -> [String]
+        split [] = []
+        split (':':xs) = split xs
+        split xs = uncurry (:) . second split . span (/= ':') $ xs
+
+getOpts :: [String] -> IO Options
+getOpts argv =
+   case getOpt Permute options argv of
+      (o,[],[]  ) -> return $ foldl (flip ($)) defaultOptions o
+      (_,_,errs) -> ioError (userError (concat errs ++ usageInfo header options))
+  where header = "Usage: fractal [OPTION...]"
+
+main = do
+        opts <- getOpts =<< getArgs
+        writePgm (fractSpec (optType opts) 254)
+                 (optBotLeft opts) (optTopRight opts)
+                 (optScale opts)

Setup.hs

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+Copyright (c) Max Rabkin
+
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions
+are met:
+
+1. Redistributions of source code must retain the above copyright
+   notice, this list of conditions and the following disclaimer.
+
+2. Redistributions in binary form must reproduce the above copyright
+   notice, this list of conditions and the following disclaimer in the
+   documentation and/or other materials provided with the distribution.
+
+3. Neither the name of the author nor the names of his contributors
+   may be used to endorse or promote products derived from this software
+   without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE CONTRIBUTORS ``AS IS'' AND ANY EXPRESS
+OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED.  IN NO EVENT SHALL THE AUTHORS OR CONTRIBUTORS BE LIABLE FOR
+ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
+STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+POSSIBILITY OF SUCH DAMAGE.

frames/1.jpg

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+The fractal program generates Newton, Julia and Mandelbrot fractals. Output is
+to standard output in PGM (Portable Graymap) format. There is currently no
+support for colour. I suggest using a general-purpose image editor such as the
+GIMP to adjust brightness levels and add colour.
+
+Fractal accepts the following options:
+
+  -s SCALE            --scale=SCALE                scale 1 unit to SCALE pixels
+                      --ll=X,Y, --lower-left=X,Y   set lower left of viewport to X,Y
+                      --tr=X,Y, --upper-right=X,Y  set upper right of viewport to X,Y
+  -m                  --mandelbrot                 render the Mandelbrot set
+  -j X,Y              --julia=X,Y                  render the Julia set at X,Y
+  -n X1,Y1:X2,Y2;...  --newton=X1,Y1:X2,Y2;...     render the Newton fractal for a polynomial with roots at X1,Y1, X2,Y2, ...
+
+(Newton fractals for functions other than polynomials are supported by the
+underlying code, but there is currently no way to specify them on the command
+line.)