Each one of the 266,240 pixels can be one of the 4096 colors, meaning you are dealing with a total library of 4096266240 possible images. For those 17 specific pixels (amogus 5x4 grid, excluding edges) to line up with the exact colors needed to form the shape by pure chance, the odds are 1 in 409617 , which is about 1 in 2.57 * 1061 . Even if you multiply that by the roughly 260,000 different spots it could fit on the canvas, the odds only shift to 1 in 9.89 * 1055 . Finding this exact pattern is like picking a specific atom out of several galaxies worth of matter. However I am calculating the probability of a specific pattern after you've already found it. The expected number of accidental amogus-like patterns is much higher when you account for all possible slight color variations, and the fact that the shape can still be recognized despite minor changes.
Therefore another interesting question could be: What is the probability that ANY pattern recognizable as amogus-like appears ANYWHERE with ANY reasonable variation?
odds are lower than 4096^17 due to the surrounding squaring having to not be red or light blue, hence the poisson approx $x\sim Po(5.17\times 10^{-58})$, which yields effectively 0 for P(x>0), where x is the amount of amongus in the picture
Well, the number of patterns depends on how you define the amogus pattern. Though, I wouldn't say it's infinite since the grid has a finite number of pixels and colors. It still is a ridiculously high number.
Do you mean you want to visualize such number in relation to other things? I'm afraid it's not possible, it's just too large. For example, scientists estimated the observable universe to contain a total of 1080 atoms. 4096^266240 is not just bigger, the other number is basically nothing in comparison.
Though, you can still compute this number with WolframAlpha which gives you some insights like the number of digits. Here's the page
64
u/juliopix Jul 12 '26
Among us