Step by Step solution about How to resolve the algorithm Ulam spiral (for primes) step by step in the Haskell programming language

The provided code is a Haskell program that uses the Ulam spiral algorithm applied to a specific range of numbers between 1 and 100. It creates a visual representation of the spiral using the Diagrams library and exports the result as an SVG image. Here's a detailed explanation of the code:

1. Importing Modules:

   • import Data.List: Provides functions for working with lists.
   • import Data.Numbers.Primes: Provides functions for checking primality.
   • import Diagrams.Prelude: Provides the Diagrams library for creating and manipulating diagrams.
   • import Diagrams.Backend.SVG.CmdLine: Allows exporting diagrams as SVG images.

2. Data Structures:

   • ulam function generates the Ulam spiral for a given range of numbers and a representation function (here, dots). It consists of two steps: swirl and map.

3. swirl Function:

   • This function takes a number n and creates a spiral pattern by alternately rotating and stacking elements of a list.
   • It first uses chop to divide the list into chunks of size n.
   • Then, it repeatedly rotates the chunks and stacks them on top of each other to form the spiral.

4. chop Function:

   • This function divides a list into chunks of a specified size.
   • It splits the list into two parts: a chunk of the specified size and the remaining part.
   • It then recursively applies itself to the remaining part to obtain all the chunks.

5. spool Function:

   • This function takes a list of lists and stacks them together in a spiral pattern.
   • It uses foldl to repeatedly accumulate elements into a table, where each row is rotated by one position to create the spiral effect.

6. showTable Function:

   • This function converts the table into a string representation, where each row is padded with spaces to ensure a consistent width.
   • It uses foldMap to apply the pad function to each row and then concatenate them into a single string.

7. dots Function:

   • This function takes a number and creates a diagram.
   • If the number is prime, it creates a black circle, and if it's not prime, it creates a white circle.

8. main Function:

   • This is the entry point of the program.
   • It generates the Ulam spiral for the range 1 to 100 using the dots representation and then creates a diagram using drawTable.
   • Finally, it exports the diagram as an SVG image using the mainWith function from the Diagrams library.

import Data.List
import Data.Numbers.Primes

ulam n representation = swirl n . map representation


swirl n = spool . take (2*(n-1)+1) . chop 1

chop n lst = let (x,(y,z)) = splitAt n <$> splitAt n lst
             in x:y:chop (n+1) z

spool = foldl (\table piece -> piece : rotate table) [[]]
  where rotate = reverse . transpose


showTable w = foldMap (putStrLn . foldMap pad)
  where pad s = take w $ s ++ repeat ' '


import Diagrams.Prelude
import Diagrams.Backend.SVG.CmdLine

drawTable tbl = foldl1 (===) $ map (foldl1 (|||)) tbl :: Diagram B

dots x = (circle 1 # if isPrime x then fc black else fc white) :: Diagram B

main = mainWith $ drawTable $ ulam 100 dots [1..]