A 1 pixel image feels like nothing. It is either black or white, so there are only two possible images. A 2 by 2 square has four pixels, and each pixel still has two choices, so it becomes 2 x 2 x 2 x 2, or 16 images.
The little trick is this: an n by n image has n squared pixels. With black and white pixels, the count is 2n2. For regular 24-bit RGB, each pixel can be one of 16,777,216 colors, so the count becomes 16,777,216n2, or the same thing written as 224n2. If transparency is included, many formats move into 32-bit RGBA, but 24-bit RGB is a solid everyday baseline for the comparison here.
Have you ever thought about a 1080p image?
A standard 1080p frame has 2,073,600 pixels. Even if every pixel were only black or white, the number of possible images would be 22,073,600. That is not just big. It is a number with more than six hundred thousand digits. A normal screen is quietly carrying a ridiculous amount of possibility.
For scale, rough science-pop estimates often put the grains of sand on Earth around 1018 to 1020, and atoms in the observable universe around 1080. A black and white 1080p image space is not merely bigger than those. It is bigger by a kind of distance our intuition is not built to walk.
1080p and 4K are already ridiculous
Writing the full numbers would make the page mostly commas, so scientific notation is kinder here. A 1080p black and white image has about 624,216 digits worth of possibilities. A 4K black and white image has about 2,496,864 digits. With regular 24-bit RGB, 1080p climbs to about 1014,981,179 possible images, and 4K climbs to about 1059,924,717.
| Resolution | Pixels | Black/white possibilities | 24-bit RGB possibilities |
|---|---|---|---|
| 1080p | 2,073,600 | ~10624,216 | ~1014,981,179 |
| 4K UHD | 8,294,400 | ~102,496,864 | ~1059,924,717 |
A 4x4 black and white universe
This tiny board has 16 pixels, so it can make 65,536 different black and white images. Tap random for a surprise, or let it walk sequentially at 60 frames per second.
At 60fps, seeing every 4x4 possibility once would take a little over 18 minutes.
Black and white pixels
Here is the count for square images from 1x1 to 10x10 when each pixel can only be black or white.
| Size | Pixels | Possible black/white images |
|---|---|---|
| 1x1 | 1 | 2 |
| 2x2 | 4 | 16 |
| 3x3 | 9 | 512 |
| 4x4 | 16 | 65,536 |
| 5x5 | 25 | 33,554,432 |
| 6x6 | 36 | 68,719,476,736 |
| 7x7 | 49 | 562,949,953,421,312 |
| 8x8 | 64 | 18,446,744,073,709,551,616 |
| 9x9 | 81 | 2,417,851,639,229,258,349,412,352 |
| 10x10 | 100 | 1,267,650,600,228,229,401,496,703,205,376 |
That last number is just for a 10 by 10 icon with no gray, no color, no transparency, no softness. Just black and white. Still, it is already enormous.
Now give every pixel regular 24-bit RGB
Now each pixel has 16,777,216 possible colors. This is closer to how we usually think about normal digital color images. Same tiny squares, but the universe gets much louder.
| Size | Pixels | Possible 24-bit RGB images |
|---|---|---|
| 1x1 | 1 | ~107 8 digits |
| 2x2 | 4 | ~1029 29 digits |
| 3x3 | 9 | ~1065 66 digits |
| 4x4 | 16 | ~10116 116 digits |
| 5x5 | 25 | ~10181 181 digits |
| 6x6 | 36 | ~10260 261 digits |
| 7x7 | 49 | ~10354 355 digits |
| 8x8 | 64 | ~10462 463 digits |
| 9x9 | 81 | ~10585 586 digits |
| 10x10 | 100 | ~10722 723 digits |
The tiny square is not tiny anymore
This is the part I enjoy. The image is still tiny enough to fit in a corner of the screen, but the number of ways it can exist has already slipped out of normal scale. Most of those images will never be drawn. Most would look like noise. A few might look like symbols, faces, maps, or something that feels oddly intentional.
That gap is the fun of it. The math says every arrangement is waiting somewhere in the count. Meaning only shows up when one of those arrangements happens to matter to us.