I have a 4K monitor, each pixel capable of 24-bit color. How many unique images can it display?
Thinking of base-10 numbers, if I have two digits, each one capable of ten different values, then I can express 10[sup]2[/sup] = 100 different numbers: 00, 01, 02, 03…99.
So if my monitor has Y pixels, and each pixel can express X different colors, then my monitor can display X[sup]Y[/sup] images.
OK, so 3840 x 2160 = 8,294,400 pixels.
24 bits of color is 2[sup]24[/sup] = 16,777,216 colors.
So my monitor can display 16,777,216[sup]8,294,400[/sup] unique images.
My calculator violently explodes when I ask it to perform that operation. There are a couple of neurons somewhere in my brain that remember it’s possible to rejigger the base and exponent into something of the form 10[sup]largenumber[/sup]. Can someone here tell me what “largenumber” is?
Your monitor buffer has 3840 x 2160 x 24 = 199065600 bits; the number you seek is 2^199065600 = 16777216^8294400 ~= 10^59924717 ~= 10^10^7.778 = 10[sup]10[sup][sup]7.778[/sup][/sup][/sup]
If you like big numbers, check out Munafo’s site. Some of his numbers are MUCH bigger than Class 3 numbers!
Sure, if I remembered how to use logs to sort that out. But all I really retained was the idea that this could somehow be done.
Plenty of great big numbers we can conceive of, but this particular one had some practical meaning outside of work on arcane theoretical mathematics - thus my interest.
Define “image”. Is a one-pixel borderless representation an “image”? If not, what defines when you’ve got enough contents to qualify as an “image”?
ETA: your monitor is not your limitation. Every pixel of it is already set to a certain value. If you opened an array of “images” and each one took up one pixel, you’d have as many “images” as pixels but the load on the monitor would be identical to what it was before.
AHunter3, I think you might have misunderstood the question. It’s not about how many different images can fit onto the screen at once. It’s about how many distinct images could be displayed, one at a time, each one filling the entire monitor (because an image that didn’t fill the entire monitor would just mean an image that did fill the monitor, with a margin of black pixels).
Personally, I categorize numbers as “big”, “astronomically big”, “combinatorically big”, and “just plain absurd”. This one is at the upper end of “combinatorically big”. Though strictly speaking, there’s some overlap between categories (like, a googol is usually astronomically big, but the largest known black holes have a lifespan of over a googol seconds, so that’s astronomical).
Sure, lots of “noise” images, and lots of images that differ from other images by one single bit, or even one single bit in multiple pixels. So the vast majority of possible images won’t be meaningful or meaningfully different from one another according to the human eye.
Speak for yourself; I thoroughly enjoyed those rites.
Within the limits of the spatial and color resolution I described it could show literally everything. It’s sort of like the monkey randomly typing on a typewriter. Hell, it could even show you that monkey and everything he types, as he’s typing it.
And some of those images would be photorealistic, and some would appear photorealistic on first glance but show telltale artifacts of Photoshopping on closer inspection, and some would be grotesque caricatures. Some would even bear watermarks identifying them as having been made using various programs, or as having been stolen from various sites (most of which programs and sites don’t even exist, of course).
Including every imaginable and unimaginable post you could write for SDMB and display on one screen. And a mindboggling number of versions of each of those posts that differ just in font and colors and noise level.
One of the possible images contains the exact text of the opening paragraphs of The Decline and Fall of the United States (2071 Edition); another is a gorgeous never-before-seen photo of Marilyn Monroe; and another shows the account numbers and passwords to access billions of Mexican cartel money …
… yet the overwhelming majority (more than 99.9999999%) of the images will be visually indistinguishable from that useless noise image!
Nitpick: Or rather a relative of that noise image. The rendition linked to has at least three flaws:
(1) It was compressed with Jpeg at a 5.2:1 compression ratio. The fine-structure of the image therefore reflects Jpeg (and probably color-transform) processing, not the desired randomness.
(2) The lower-resolution versions of the big image are spatial averages, destroying the pretense of randomness.
(3) The average component value should be 127.5 (the mean over 0,1,2,…,255) but is instead 127.0. This was caused by this faulty line in the posted python code:array = numpy.random.rand(height, width, 3) * 255
What’s the problem with that line? I’m just starting to learn python, but wouldn’t that that rand command generate a a value between zero and one, inclusive?
Moreover, the average of all component values from all possible 24-bit images of a given height and width must be 127.5, but since any single image is just a sample from that whole population, shouldn’t it be possible for any single image to have an average component value other than 127.5? Afterall, a random image generator is just as likely to create an all-black or all-white image as it is to create the exact image seen at that link.
