显示haskell中的mandelbrot集合时出现逻辑错误

Question

我创建了一个程序，它的目的是绘制一个分形集( manderbrot集)，它不包含任何语法错误，但只出现一个像素，而不是集。

下面是我的程序：

module Main where

import Graphics.UI.Gtk
import Graphics.UI.Gtk.Builder()
import Graphics.Rendering.Cairo as C
import Control.Monad (when)


main :: IO()
main = do
    _ <- initGUI
    builder <- builderNew
    builderAddFromFile builder "09-mandelbrot.ui"

    window   <- builderGetObject builder castToWindow "Figure de Mandelbrot"
    canvas <- builderGetObject builder castToDrawingArea "drawingarea1"
    _ <- onExpose canvas $ const (updateCanvas canvas) 

    widgetShowAll window
    mainGUI


updateCanvas :: DrawingArea -> IO Bool
updateCanvas canvas = do
  win <- widgetGetDrawWindow canvas
  (width, height) <- widgetGetSize canvas
  renderWithDrawable win $ example (fromIntegral width) (fromIntegral height)
  return True

k=100

mandelbrot :: Double -> Double -> Bool
mandelbrot a b = 
  let 
    mandelrec :: Double -> Double -> Int -> Bool 
    mandelrec x y i
      | (x * x + y * y > 4) = False
      | (i==k) && (x * x + y * y <= 4) = True
      | otherwise = mandelrec x' y' (i+1)
            where x' = x * x - y * y + a
                  y' = 2 * x * y + b
  in mandelrec 0 0 0

affiche :: (Double, Double) -> Render()
affiche (a, b) = when (mandelbrot a b) $ C.rectangle a b 1 1

colonnes w = [ t/w*4-2 | t<-[0..(w-1)] ]
lignes h = [ t/h*4-2 | t<-[0..(h-1)] ]


example :: Double -> Double -> C.Render ()
example width height = do
    setSourceRGB 0 0 0
    setLineWidth 1

    mapM_ affiche (zip (colonnes width) (lignes height))
    stroke

如果需要的话，我可以给你解释。我已经测试了lignes和colonnes函数，看起来没问题。

Answer 1

好了，它现在起作用了。

我没有收集范围-2..2中的所有点，但只收集了那些放置在对角线上的点。

下面是一个有效的代码：

module Main where

import Graphics.UI.Gtk
import Graphics.UI.Gtk.Builder()
import Graphics.Rendering.Cairo as C
import Control.Monad (when)


main :: IO()
main = do
    _ <- initGUI
    builder <- builderNew
    builderAddFromFile builder "09-mandelbrot.ui"

    window   <- builderGetObject builder castToWindow "Figure de Mandelbrot"
    canvas <- builderGetObject builder castToDrawingArea "drawingarea1"
    _ <- onExpose canvas $ const (updateCanvas canvas) 

    widgetShowAll window
    mainGUI


updateCanvas :: DrawingArea -> IO Bool
updateCanvas canvas = do
  win <- widgetGetDrawWindow canvas
  (width, height) <- widgetGetSize canvas
  renderWithDrawable win $ example (fromIntegral width) (fromIntegral height)
  return True

k :: Int
k=100

mandelbrot :: Double -> Double -> Bool
mandelbrot a b = 
  let 
    mandelrec :: Double -> Double -> Int -> Bool 
    mandelrec x y i
      | (x * x + y * y > 4) = False
      | (i==k) && (x * x + y * y <= 4) = True
      | otherwise = mandelrec x' y' (i+1)
            where x' = x * x - y * y + a
                  y' = 2 * x * y + b
  in mandelrec 0 0 0

affiche2 :: Double -> Double -> Render()
affiche2 a b = do
  C.rectangle a b 1 1
  stroke

affiche :: ((Double,Double), (Double,Double)) -> Render()
affiche ((a0,a), (b0,b)) = when (mandelbrot a b) $ affiche2 a0 b0

colonnes w = [ (t,t/w*4-2) | t<-[0..(w-1)] ]
lignes h = [ (t,t/h*4-2) | t<-[0..(h-1)] ]
points w h = [ (colonne,ligne)| colonne <- colonnes w,ligne <- lignes h]

example :: Double -> Double -> C.Render ()
example width height = do
    setSourceRGB 0 0 0
    setLineWidth 1

    mapM_ affiche (points width height)
    stroke