I called this the Rose Spiral because of my first impression of it. The spiral was full of those nice little rose-like spirals that come our so often in these images. Well here are a few from this same equation:
$eq=(round(sqrt($num*$i)*($num))%3==0)
Where $x,$y are the coordinate points, $num is the place on the Ulam Spiral, and $i is the multiplier (noted below each image). And this is the result:
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