Mandelbrot Runner in BechML

mandelbrot.bml

use Core.*;

scale : int := 1000;

xMin : int := Int.sub 0 2500;
xMax : int := 1000;
yMin : int := Int.sub 0 1750;
yMax : int := 1750;

width : int := 80;
height : int := 80;

maxIter : int := 50;

escapeSquared : int := 4000000;

getChar : int -> string := \n ->
  if Int.eq n maxIter then "#"
  else if Int.lt n 5 then " "
  else if Int.lt n 10 then "."
  else if Int.lt n 15 then ":"
  else if Int.lt n 20 then "-"
  else if Int.lt n 25 then "="
  else if Int.lt n 30 then "o"
  else if Int.lt n 35 then "O"
  else if Int.lt n 40 then "@"
  else "#";

squaredScaled : int -> int := \x -> Int.div (Int.mul x x) scale;

mandelbrotStep : int -> int -> int -> int -> int -> int := \cRe cIm zRe zIm iter ->
  if Int.geq iter maxIter then maxIter
  else
    (\zReSquared zImSquared ->
      (\magnitude ->
        if Int.gt magnitude escapeSquared then iter
        else
          (\newRe newIm ->
            mandelbrotStep cRe cIm newRe newIm (Int.add iter 1)
          ) (Int.add (Int.sub zReSquared zImSquared) cRe)
            (Int.add (Int.div (Int.mul (Int.mul 2 zRe) zIm) scale) cIm)
      ) (Int.add zReSquared zImSquared)
    ) (squaredScaled zRe) (squaredScaled zIm);

computePoint : int -> int -> int := \cRe cIm ->
  mandelbrotStep cRe cIm 0 0 0;

xRange : int := Int.sub xMax xMin;
yRange : int := Int.sub yMax yMin;

printPixel : int -> int -> io () := \y col ->
  (\cRe cIm ->
    (\iters ->
      IO.print (getChar iters)
    ) (computePoint cRe cIm)
  ) (Int.add xMin (Int.div (Int.mul col xRange) width))
    (Int.add yMin (Int.div (Int.mul y yRange) height));

printRowPixels : int -> int -> io () := \y col ->
  if Int.geq col width then IO.print ""
  else
    IO.monad.bind (printPixel y col) (\_ ->
      printRowPixels y (Int.add col 1));

printRows : int -> io () := \y ->
  if Int.geq y height then IO.applicative.pure ()
  else
    IO.monad.bind (printRowPixels y 0) (\_ ->
      printRows (Int.add y 1));

main : io () := printRows 0;