From the GD documentation:

$index = $image->colorAllocate(red,green,blue)

This allocates a color with the specified red, green and blue components and returns its index in the color table, if specified. The first color allocated in this way becomes the image's background color. (255,255,255) is white (all pixels on). (0,0,0) is black (all pixels off). (255,0,0) is fully saturated red. (127,127,127) is 50% gray. You can find plenty of examples in /usr/X11/lib/X11/rgb.txt.

(emphasis is mine)

So, before your loop do:

$im->colorAllocate(255,255,255);
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