Simple combinatorics about an 8 MegaPixel shot

x2thay

Hello there,

So consider an 8 megapixel picture (res: 3264x2448).
Now, it seems rather simple but I just can't figure out how to calculate the entire number of possible shots/photographs one can take within that resolution, assuming each pixel can have 16777216 different values/colors.

jbriggs444

How many possibilities for a 1 pixel picture?
How many possibilities for a 2 pixel picture?
How many possibilities for a 3 pixel picture?
Can you generalize to n pixels?

bahamagreen

You have 7990272 pixels, each of which can have 16777216 values.

If you string the pixels out in a line, then it is like an odometer with 7990272 wheels and each wheel has 16777216 numbers on it.

So the base of this odometer is base 16777216 and the number you want has "16777216" (the largest "digit" in this base) in each position, and there are 7990272 positions with this "digit" in the number.

So the number you want is the base raised to the power of the number of pixels:

16777216^7990272

Wolfram says in base 10 it would be about 1.23X10^57727477

This is kind of a neat problem because the images include all possible images, all possible zooms in and out to any arbitrary degree, all possible angles, all possible distortions, of all possible subjects, backgrounds, compositions, scales, etc. Pretty mind boggling.

micromass

It also contains all the faces of all the people who ever lived and who ever will live!!

bahamagreen

Yes, plus all the faces of every creature including every alien race in all the inhabited places in the history of the universe.

And if you scroll through it in the right order, it shows everything ever written, or yet to be written, in every font, includes every formula, derivation, graph, proof, and sequence.

If you scrolled through it in the right order at a fast enough presentation of images, it would also show every movie and TV show ever made, including out takes, and different variations on plots. etc.

A question that is suggesting itself to me...

Doesn't this seem to be similar to the concept of phase space?

Or as expressed in the eight postulate of "It's Easy" by the Beatles: "Nothing you can see that isn't shown"

fortissimo

The vast majority of these images will all be senseless noise, though.

micromass

Or will they??? Dun dun duuuuuuuun...

micromass

OK, I did the test and I generated a random image. I got the following:



So it seems you're right. We do get senseless noise.