^ actually it's a little less than that if you factor out trivial transformations (horizontal / vertical flip, rotate +90 or -90 degrees). Roughly divides it by 8, so, 2^61 for binary images. You can probably also factor out inversions, so 2^60 (roughly 1.1 billion billion (1152921504606846976)). Also, factoring out simple offsets of the same pattern divides by either 49 or 64 (don't remember which calculation is correct), leading to either 2^54.385 or 2^54.
Then much of the remainder is still just bitnoise. A rough test based on requiring the image to have at least 4 2-bit runs (that is, 11 or 00), 3 3-bit runs, 2 4-bit runs, and 1 5bit run, over 10000 random input images, classifies roughly 1864 of them (18%) as interesting.
This would lead to an estimated number of potentially-interesting 1bit 8x8 images equalling ~2^51.576 (3,357,883,882,167,442 or 3.3 million billion.)
For 16-color images, the base number would be 256bit rather than 64bit, leading to an estimated number of potentially-interesting images equalling ~2^244.576
(a 74-digit number). A more sophisticated classifier (based on clusters rather than scanlines) might get that down to 2^240.
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