All the frames in the world!

The email about watching all the possible frames in a 1080 screen on this weeks podcast drove me to crunching some numbers.

No one has corrected me on my stupid errors yet. Good. It should of course be 2^24^(1920*1080) which is 2^49766400, a number so large no software I have can process it. Sorry for the previously optimistic results. Trillions turned out to be way, way too low. As for time, I suspect the universe will have ended before you are done watching the whole thing, regardless of framerate.

If we assume 24-bit color depth, that is 16 777 216 possible colors for a single pixel, and a screen of 1080x1920 pixels, the total number of combinations of these pixels is 2^24*1080*1920. Which equals approximately 3.47*10^13 frames, or 34.7 trillion.

This means that watching the past, present, and future in glorious HD-quality would take about 1.1 million years, if watching one frame per second.

Reducing the color depth, or, as mentioned, reducing the resolution will obviously have a dramatic effect on this number. 8-bit colordepth frames at 560x720 will only take about 3 years and 3 months. Although 256 colors don't describe the real world very well, so don't think you have seen it all just because you did this stupid stupid thing.

If anyone is noticing any errors in these calculations feel free to correct me. I'm NOW pretty confident in these numbers, but I do make mistakes occasionaly.

But but but, we could go to 60fps if we use a PS4 for the calculation, right?

Kidding. Love that somebody was smart enough to get us these number.

Yea, why can't we go 60 FPS for this? Then it would only take (1.1/60) million years.

How funny if the human race had input lag .

Wouldn't most of the images just be incomprehensible amalgamations comprised of interspersed points of light-emitting photons?

I'm no maths person, so I don't really get your calculation. What's the reason that your initial calculation of 16,777,216 (possible colours) x 2,073,600 (available pixels) isn't correct (34,789,235,097,600)?

@senormartinez: The number's not incalculable - it's 1.500416922648713659562119353861314698489596010100536668539209917652... × 10^14981179 and, expanded, only 14,981,180 digits long or about 15 MB of information (thanks, Mathematica).

@beachthunder: The pixels are separate. Multiplying gives you the number of alternatives for having every pixel be every colour, but only turning on one pixel at a time. Raising to a power gives the number of alternatives for using all pixels at the same time. Think of it with a much smaller screen of 6 pixels and 8 colours - one by one, each of the 6 pixels can display 8 colours = 6 x 8 combinations, or 48. If you use them all at once, there's 8 choices x 8 choices x 8 choices x ... 6 times = 8^6, or 262,144.

ETA: I got curious. You can easily get a decent value with logs and exponents, but I figured I'd check how easy it was to calculate the whole thing. A test in Haskell came up with the answer in "(24.97 secs, 3063390580 bytes)" - the number is only 15 MB long, but it needed about 3 GB to calculate it on my several-year-old Core 2 Duo computer. (Why Haskell if I just used Mathematica? Well, I don't have the latter on my computer right now, I used Wolfram Alpha before but it's basically the same for this.)

ETA: Tada