I wrote a paper about doing this using human eyes as the "repeating pattern" (either someone else's, or your own in a mirror):
https://philpapers.org/archive/ALEDSK.pdf ...You can use this trick to make boring meetings or conversations mildly more amusing (but be careful not to look like a clown crossing your eyes).
If you're an expert at this, you can even do it to your own hands. Hold both hands in front of you but with one of them palm-away and one of them palm-toward you, so that they have the same shape, then cross- or parallel-view them to get an illusionary middle third hand. Walk around while focusing on the third hand and it's a seriously trippy effect.
Another "super power" application similar to OP: the ability to confirm whether or not two distant digital clocks' seconds-digits are perfectly in sync. Since they're distant, it takes time to shift one's gaze from one to the other, making it hard to confirm whether they're in sync. But cross your eyes so as to reduce the distance, and voila.
Yet another application: quickly assume the same head-tilt angle as your conversation partner. Suppose they tilt their head to the left by N degrees and you want to tilt yours the same way, how can you be sure you have the exact correct tilt? Easy: parallel-view their eyes (as described in the aforementioned paper). You will HAVE to tilt your head the same as them in order to see their "third eye" (and once you've locked on to their third eye, you can effortlessly adjust your head tilt as they do by using their third eye as the necessary guide)
