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We Have Pictures of That™

The contents of this page is not humorous in any fashion, so reading it is purely for your own enjoyment. Read at your own risk. It is not my fault if you think about the possibilities of such a formula. You have been warned.


Summer 2002, I was watching this strange, America-themed motorcyclist drunkenly dance. He was very large and his clothes were about to break, but he had an interesting command of his Santa Claus-esque stature, and I wished that I had a video camera to capture his new form of Irish jig. I would need a small video camera. He would never know I was capturing his performance, but then I realized that wasn't feasible and the only way I could ever get this scene back would be if I could digitally recreate it on the computer.

I automatically shunned this thought. It would take forever, and it wouldn't be worth it. My synapses fired rapidly as I thought of an idea to remedy this unimportant problem (his dancing really affected me. or not). What I stumbled across was fabulous, however also nearly impossible for my current resources to do. Read on...


PART 1: THE BASICS

In order to grasp this theory, first, let's make sure you understand what a pixel is! Put your mouse over one of the buttons on the left of this page. The entire button (including the surrounding white-blue area) is 109 x 29 pixels (for a total of 3,161 square pixels). This is easy so far, right?

A pixel is the smallest graphical representation unit on a computer (pixel - picture element). Have you ever resized your desktop from 640x480 to 800x600 or 1024x768 or some other resolution? These measurements determine how many pixels your monitor shows. When your monitor is at a lower resolution (lower being more towards 640x480), pixels are way easier to see without squinting or putting your face right up to the glass. This is mostly because of your monitor's native resolution (the resolution that maps each computer pixel 1:1 for a pixel your monitor is physically capable of displaying).

Now, a pixel can hold different color information based on how the computer is set up. A pixel can hold 2 colors (black and white), 16 colors (basic shades of red, green, blue, etc.), 256 colors (same as 16 but more expanded), 256 colors (grayscale), 16,777,216 million colors (most common setup) or higher. Within these color ranges, all things you see on your computer can be shown. A photo from a digital camera, a scanned photo, or a digitally-created imageis stored in pixels. Therefore, a picture on the computer is REALLY just an array of pixels.

Now for a visual demonstration:

This is a 5 x 5 pixel (25) image. There are 24 pixels of pure white and only 1 pixel that is black. Notice how incredibly small a pixel is.

Different color palettes (more common ones: 2, 16, 256, 16,777,216) produce images that look similar, but the more colors in the palette, the higher quality the image will be... Also, two color palettes do not have to be only black and white, that is just the most common use. Also, just because a palette may have 16 million colors, it doesn't mean that every picture will use them all, or even most of them.

16,777,216 color palette.
16 color palette
2 color palette

These images each have 14,391 pixels


Part 2: CHOICES AND EXPONENTS

In math, you probably learned about how to calculate the number of possible combinations you could have of a certain number of choices. Let's review this really quick: If you have two different pairs of pants and two different shirts to wear, here is how you figure out how many different combinations you have: two pants x two shirts = four outfit choices .

Now, the more choices you have, the more final combinations there would be. If you are going to order a pizza, and you have the choice of THREE different toppings, THREE different crusts, and THREE different cheeses, that's a total of twenty-seven choices, right? 3 x 3 x 3 = 33 = 27?

Visual demonstration:

If there are three categories of four choices, and only one may be picked from each category, how many total combinations can be made?

CATEGORY 1:

A B C D

CATEGORY 2:

E F G H

CATEGORY 3:

I J K L

RESULT:

AEI
AEJ
AEK
AEL
AFI
AFJ
AFK
AFL

AGI
AGJ
AGK
AGL
AHI
AHJ
AHK
AHL

BEI
BEJ
BEK
BEL
BFI
BFJ
BFK
BFL

BGI
BGJ
BGK
BGL
BHI
BHJ
BHK
BHL

CEI
CEJ
CEK
CEL
CFI
CFJ
CFK
CFL

CGI
CGJ
CGK
CGL
CHI
CHJ
CHK
CHL

DEI
DEJ
DEK
DEL
DFI
DFJ
DFK
DFL

DGI
DGJ
DGK
DGL
DHI
DHJ
DHK
DHL

Answer: 64

4 x 4 x 4 is the SAME thing as 43, which is 64



Part 3: PUT THIS TOGETHER

Well, back to my story now. I got to thinking about all of the above information, and I realized that using a computer (or a string of computers), ALL PICTURES possible could be created. "Yeah, sure," you're thinking, or maybe even, "That's useless," but...

Here are the facts we've established:

  • Pixels are the smallest graphical unit in a picture and all pictures are just combinations of pixels
  • Combinations may be represented by exponential calculations

So, with this information... A computer program could be created which cycles through every single pixel in a given picture size and assigns each pixel to EVERY SINGLE color combination possible. The most common, and most realistic-looking, color palette that we have discussed is the 16 million color palette (approx. 256 shades of red, green, and blue for a total of 16,777,216 colors), and the second best choice for such a project would be a 256-color grayscale palette (all shades of black, grey, and white), so for the rest of the example, these will be the only two focused on. Sure, other palettes would work, but if the computer cycles are to be used for such a project, no need to waste them on poorly-colored OR ultra-pristine (higher than 16-bit) pictures, right?

Some related fun, view a randomly created 32x32 image in three different color depths, each takes some time to load, so be patient.
32x32 - Black and White
32x32 - Grayscale
32x32 - 16 million+ colors

There is no set resolution or standard for implementing this, but for purposes of my example, let's use the NTSC digital video standard. This resolution is 720 x 480 pixels. It is close to the aspect ratio of a normal film photograph, and being a digital video resolution, proper storage, such as DVD-Video or even storage of these pictures on a digital video camera would be feasible (provided that we can ignore compression artifacts).

So, 720x480 pixels is a total of 345,600 pixels! This is where the problem comes in. Look at these exponents:

GRAYSCALE (256 colors)-
256345,600

FULL COLOR (16,777,216 colors) -
16,777,216345,600

Yes, that is a very large number, but think of this... A program like Maple can calculate it, but the result is a little too large for me to put on here. The interesting thing though is that it is a finite number, and it would be a representation of every picture ever (and all of the smaller parts of larger pictures, etc.)


Part 4: THE FINAL PROBLEMS

The execution of this theory is difficult because of a few more problems. Once the number of pictures is calculated, it must be figured out how to store these pictures. An uncompressed 720x480 full-color 16-bit image takes up approximately 1,036,854 bytes. Storage is definitely a problem.

At the same time, this idea might be illegal (sadly). Every single image possible would be generated... In every angle, every variation. No more new artistic innovation would be necessary, it'd all be there. Every single frame for movies of your life would be created, every variation of your life would be created. Every variation of everyone's life... illegal images would also be produced, such as child pornography.

Also, not every image produced would be a discernable picture! A small fraction of the images would be even worth keeping, and who would sort through them? How many lifetimes would it take to do this?

This was just an idea I had one day, and I find it very interesting. Hopefully my small primer has planted the seed in your mind :)

For another discussion of this idea, check out Jordan Upham's.