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From what i can see you are using a 3x3 as a pixel....if you shift the 3x3 each frame by 2 pixels in both x and y you can achieve an effective "screen resolution".  FYI  2/3 is a Fibonacci ratio... but as mentioned you will benefit from an aspect ratio longer in the vertical. Perhaps a 2Hx5V  with the pixel shifting 3H and 8V each frame(again this is using Fibonacci)

I can see you are using 4? colours in your random colour...if you use 3(RGB) you should be able to implement full colour. Just split your actual colour "randomly"(phi) across both images in a "randomly" cycling an average of the actual colour.

 Full colour and full screen resolution are the easier bit.

Infinite depth is possible when each frame consists of part of an image from each depth.

At the moment you are displaying 16? depths on each display 16 shifting depths..... shift the depth of each of those depths by a fraction of 0.618(phi) of the space between each depth but only render part of each depth in  a "random" distributed cycle across the screen.. so each 2x5 pixel on one frame either side of the screen has a partner(or at most a partner in the frame before of after it), but each adjacent 2x5 pixel will likely represent a different depth and each pixel on the screen is likely changing on each frame..... this should give you your "infinite" depth auto stereogram.   ( limited only by the screen resolution)

Phi is irrational and will be impossible to work with so using the rational Fibonacci's will make this possible :

0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584,