Picture This

Okay, so I hope the basic idea is clear. This imaginary device simply brute-force generates every possible image for the resolution and colors we specified. It just keeps spitting out images, you see; I imagine them in a sort of slide show carousel.

We are going to be dealing with a very large number here in a minute—but not to worry, it isn’t infinity, you won’t need any special equipment—and we’re not going to get all “mathy” or anything either.

Previously I suggested an image size that would provide enough space for details about the subject of the image to be detected, but the size itself is immaterial for our discussion, as you will later see. Let’s use the same aspect ratio, but reduce the size again by half. 16:9 reduces neatly to a 400 x 225 grid, giving us 90,000 pixels.

So, every single 90,000 pixel image, with each pixel having one of 256 different possible grey tones, would total exactly how many images? Happily, a simple formula gives us the answer: 90,000^ 256, that is the number of items (pixels) raised to the power of the number of possible values (grey tones).

Which equals (warning: here is that very large number):

193,233,498,322,889,151,054,540,687,220,195,810,554,014,657,616,033,285,501,845,376,289,024,667,464,155,370,000,179,394,297,860,293,543,900,823,292,945,861,195,051,535,091,013,329,408,840,980,404,787,286,395,425,605,501,337,273,994,827,780,623,224,073,723,381,210,433,996,682,422,765,917,915,046,589,858,829,952,724,365,414,410,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. ▶ That escalated quickly!

Typically numbers this large are written as little equations themselves, i.e. in scientific notation, so that monsters like the one above can be appreciated through a more reasonable representational lens. So let’s do that, and let’s also round it down a bit. Which gives us ~1.93 e^1,268. Even rounded down, still—a shit-ton. I think these calculations are correct, give or take a kajillion-billion-zillion. Maybe check here if in doubt: Combinations and Permutations, Scientific Notation.

Honestly I hope you are not too annoyed, having payed attention to all the above, when I now tell you that the device itself is not really the point. It is the set of images it generates which we want to consider. And the first important thing about this set is, although quite humongous, it is not infinite. This will be important later when we are selecting interesting images.

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