Simple combinatorics about an 8 MegaPixel shot

  • Context: Undergrad 
  • Thread starter Thread starter x2thay
  • Start date Start date
  • Tags Tags
    Combinatorics
Click For Summary

Discussion Overview

The discussion revolves around the combinatorial possibilities of an 8 megapixel image, specifically exploring how many different images can be generated given a resolution of 3264x2448 pixels, with each pixel capable of displaying 16777216 different colors. The scope includes theoretical calculations and implications of these possibilities.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant questions how to calculate the total number of possible photographs for an 8 megapixel image, given the color options for each pixel.
  • Another participant suggests that the total number of combinations can be represented as 16777216 raised to the power of 7990272, indicating the vast number of potential images.
  • Some participants express awe at the implications of this calculation, noting that it encompasses all conceivable images, angles, and distortions.
  • There is a suggestion that this concept relates to phase space, with references to the idea that all possible visual representations could be included.
  • One participant humorously notes that despite the vast number of combinations, most images would likely be meaningless noise.
  • Another participant confirms the generation of a random image resulted in senseless noise, supporting the previous claim about the nature of most images.

Areas of Agreement / Disagreement

Participants generally agree on the mathematical representation of the problem and the vastness of the possibilities, but there is a playful debate about the meaningfulness of the generated images, with some asserting that most would be noise while others question this assumption.

Contextual Notes

The discussion does not resolve the implications of the vast number of images or the nature of noise versus meaningful content, leaving these aspects open for further exploration.

x2thay
Messages
14
Reaction score
0
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.
 
Physics news on Phys.org
x2thay said:
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.

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?
 
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.
 
bahamagreen said:
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.

It also contains all the faces of all the people who ever lived and who ever will live!
 
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"
 
Last edited:
The vast majority of these images will all be senseless noise, though.
 
fortissimo said:
The vast majority of these images will all be senseless noise, though.

Or will they? Dun dun duuuuuuuun...
 
fortissimo said:
The vast majority of these images will all be senseless noise, though.

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

images?q=tbn:ANd9GcTIdJiiCUhJ2WZRnFLvQiFgD4ynv7FI0BJxENb--tjqq7kKkttu5g.jpg


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

Similar threads

  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 7 ·
Replies
7
Views
4K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 17 ·
Replies
17
Views
3K
  • · Replies 6 ·
Replies
6
Views
4K
  • · Replies 1 ·
Replies
1
Views
13K