Step by Step solution about How to resolve the algorithm Barnsley fern step by step in the Haskell programming language

This Haskell code generates a Barnsley fern, a fractal pattern that resembles a plant. It uses a combination of random numbers and affine transformations to create the fern's characteristic shape.

The code begins by importing several modules:

• Data.List for the scanl' function, which is used to accumulate values in a list.
• Diagrams.Backend.Rasterific.CmdLine for the mainWith function, which is used to generate a PNG image of the fern.
• Diagrams.Prelude for the frame and diagramFrom functions, which are used to create a Diagram object.
• System.Random for the getStdGen and randomRs functions, which are used to generate random numbers.

The code then defines four affine transformations, f1, f2, f3, and f4, which are used to transform points on the plane. These transformations are used to create the fern's characteristic shape.

The func function takes a point and a random number as input and returns a new point that has been transformed by one of the four affine transformations. The function fern takes a list of random numbers as input and returns a list of points that have been transformed by the func function.

The drawFern function takes a list of random numbers and a count as input and returns a Diagram object that represents the fern. The function diagramFrom takes a list of points and a function that draws a point as input and returns a Diagram object that represents the points. The function dot is used to draw a point as a small circle.

The main function generates a list of random numbers and a count and then calls the drawFern function to create a Diagram object. The mainWith function is then used to generate a PNG image of the fern.

Here is an example of how to use the code to generate a PNG image of a fern:

fern -o fern.png -w 640 -h 640 50000

This command will generate a PNG image of a fern with a width of 640 pixels, a height of 640 pixels, and 50000 points.

import Data.List (scanl')
import Diagrams.Backend.Rasterific.CmdLine
import Diagrams.Prelude
import System.Random

type Pt  = (Double, Double)

-- Four affine transformations used to produce a Barnsley fern.
f1, f2, f3, f4 :: Pt -> Pt
f1 (x, y) = (                       0,             0.16 * y)
f2 (x, y) = ( 0.85 * x + 0.04 * y    , -0.04 * x + 0.85 * y + 1.60)
f3 (x, y) = ( 0.20 * x - 0.26 * y    ,  0.23 * x + 0.22 * y + 1.60)
f4 (x, y) = (-0.15 * x + 0.28 * y    ,  0.26 * x + 0.24 * y + 0.44)

-- Given a random number in [0, 1) transform an initial point by a randomly
-- chosen function.
func :: Pt -> Double -> Pt
func p r | r < 0.01  = f1 p
         | r < 0.86  = f2 p
         | r < 0.93  = f3 p
         | otherwise = f4 p

-- Using a sequence of uniformly distributed random numbers in [0, 1) return
-- the same number of points in the fern.
fern :: [Double] -> [Pt]
fern = scanl' func (0, 0)

-- Given a supply of random values and a count, generate a diagram of a fern
-- composed of that number of points.
drawFern :: [Double] -> Int -> Diagram B
drawFern rs n = frame 0.5 . diagramFrom . take n $ fern rs
  where diagramFrom = flip atPoints (repeat dot) . map p2
        dot = circle 0.005 # lc green

-- To generate a PNG image of a fern, call this program like:
--
--   fern -o fern.png -w 640 -h 640 50000
--
-- where the arguments specify the width, height and number of points in the
-- image.
main :: IO ()
main = do
  rand <- getStdGen
  mainWith $ drawFern (randomRs (0, 1) rand)