Mandelbrot Lambda

mandelbrot.lambda

/*
Name:  Mandelbrot Set (Mandelbrot)
Description:  Generates a Mandelbrot set based on given assumptions that can be used with conditional formatting to view the visual representation.
Parameters:
   xleft - Left X value
   xright - Right X value
   ytop - Top Y value
   ybottom - Bottom Y value
   size - number of columns/rows in square output range
   iterations - number of iterations
Source:  Excel Robot (@ExcelRobot), inspired by Chris Rae's video: https://www.youtube.com/watch?v=v3BtrlSOrX0
*/
Mandelbrot = LAMBDA(xleft,xright,ytop,ybottom,size,iterations,
   MAKEARRAY(size,size,LAMBDA(c,r,LET(
      x0, xleft+(r-1)*(xright-xleft)/size,
      y0, ytop+(c-1)*(ybottom-ytop)/size,
      fn, LAMBDA(ixy,iteration,LET(
         i, INDEX(ixy,,1),
         x, INDEX(ixy,,2),
         y, INDEX(ixy,,3),
         repeat, AND((x*x+y*y)<=(2*2),i>=iteration-1),
         newi, IF(repeat,iteration,IF(i<iteration,i,i-1)),
         xtemp, IF(repeat,x*x-y*y+x0,0),
         newy, IF(repeat,2*x*y+y0,0),
         newx, xtemp,
         CHOOSE({1,2,3},newi,newx,newy)
      )),
   INDEX(REDUCE({0,0,0},SEQUENCE(iterations),fn),1)
   )))
);

Revised replacing CRLF line endings with just LF because AFE wasn't sync'ing properly after import.

To reproduce the conditional formatting used in animated GIF:

1. If cell value is equal to number of iterations, set fill color to black. And check the Stop option so it won't apply any additional conditional formats.
   

2. Apply 3-color scale gradient using black/purple/yellow.