In the previous note by -> lukeross at sys3175 dot co dot uk <- there is a coding error in the for() loops. After correcting the error, I found that this function did a great job of  converting color images to 2 colors.
The following is the corrected function code:

function ImageColorFloydSteinberg($dst_img, $src_img) {
    ImageColorAllocate($dst_img, 0,0,0);
    ImageColorAllocate($dst_img, 255,255,255);
    $isx = ImageSX($src_img);
    $isy = ImageSY($src_img);
    $grey_img = ImageCreate($isx, $isy);
    for ($a = 0; $a <= 255; $a++) ImageColorAllocate($grey_img, $a,$a,$a);
    $isx -= 1; // To correct pixel count in source image width starting from 0
    $isy -= 1; // Correcting pixel count in source image height starting from 0
    for($x = 0; $x <= $isx; $x++) {
        for($y = 0; $y <= $isy; $y++) {
            $color = ImageColorsForIndex($src_img, ImageColorAt($src_img, $x, $y));
            $greyscale = .299 * $color["red"] + .587 * $color["green"] + .114 * $color["blue"];
            ImageSetPixel($grey_img, $x, $y, ImageColorClosest($grey_img, $greyscale, $greyscale, $greyscale));
        }
    }
    for($x = 0; $x <= $isx; $x++) {
        for($y = 0; $y <= $isy; $y++) {
            $color = ImageColorsForIndex($grey_img, ImageColorAt($grey_img, $x, $y));
            if ($color["red"] > 128) {
                ImageSetPixel($dst_img, $x, $y, ImageColorClosest($dst_img,255,255,255));
                $err = $color["red"] - 255;
            } else {
                ImageSetPixel($dst_img, $x, $y, ImageColorClosest($dst_img,0,0,0));
                $err = $color["red"];
            }
            if ($x != $isx) {
                $color2 = ImageColorsForIndex($grey_img, ImageColorAt($grey_img, $x+1, $y));
                $newgrey = $color2["red"] + $err * 7 / 16;
                ImageSetPixel($grey_img, $x+1, $y, ImageColorClosest($grey_img,$newgrey, $newgrey, $newgrey));
            }
            if ($x != 0) {
                $color2 = ImageColorsForIndex($grey_img, ImageColorAt($grey_img, $x-1, $y));
                $newgrey = $color2["red"] + $err * 3 / 16;
                ImageSetPixel($grey_img, $x-1, $y, ImageColorClosest($grey_img,$newgrey, $newgrey, $newgrey));
            }
            if ($y != $isy) {
                $color2 = ImageColorsForIndex($grey_img, ImageColorAt($grey_img, $x, $y+1));
                $newgrey = $color2["red"] + $err * 5 / 16;
                ImageSetPixel($grey_img, $x, $y+1, ImageColorClosest($grey_img,$newgrey, $newgrey, $newgrey));
            }
            if ($x != $isx && $y != $isy) {
                $color2 = ImageColorsForIndex($grey_img, ImageColorAt($grey_img, $x+1, $y+1));
                $newgrey = $color2["red"] + $err / 16;
                ImageSetPixel($grey_img, $x+1, $y+1, ImageColorClosest($grey_img,$newgrey, $newgrey, $newgrey));
            }
           
        }
    }
    imagedestroy($grey_img);
}