Now think of this, when you take pictures of anything, unless you take a picture of something completely stationary with no changes in lighting between pictures, the picture will almost always be different. When you record a video, you are taking a sequence of hundreds to thousands of different still images, each of which would take up a different combination of pixels of various colors.
This is series of frames playing one after another at 10 frames per second.
What's important here, is that this animation takes up 6 different frames, 6 different images. Now going back to 1bpp color depth, how many possible different "frames" could you have if you had a monitor with a resolution of 2x2 pixels? With two possible colors, you can calculate the answer which is (2^1)^(2*2) or two to the power of color depth to the power of the resolution/number of pixels or 16. And just to make sure, you can look at this picture:
So, (2^24)^(1920*1080) would give you the number of images that could be projected onto my monitor.
Just to show how high that goes:
(2^24)^(2,073,600)
16,777,216^(2,073,600)
2^1 = 2
2^2 = 4
2^3 = 8
16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192 <-- this is how far I know by memory, which is 2^13. We know from our color depth that 2^24 is 16 million. 16 million squared is 281,474,976,710,656 which is already in the trillions and 16 million^2 million would likely be too large to even fit in this post.
To give another example of how this works out:
(2^1)^(2*3) is 64.
(3)^(1x1) is 3
(3)^(2x1) is 9
(number of colors)^(number of pixels)
An SNES's screen resolution is 256x224, which is already 57,344 pixels.
The SNES also has various emulation modes. One in particular is Mode 7 which is 8-bit (256 colors). Every pixel is represented by its own byte (hence, 8bpp or 8 bits per pixel). Each pixel can have 256 colors (0x00 to 0xFF).
The hex data shown in the hex editor would actually point to the palette of colors to choose from. 26 would be the 26th color starting from 0. I'd make a screenshot of my actual palette data for this, but I don't feel like going through Lunar Magic to do that.
Each of the colors shown in this 16x16 palette could be any other of the 256 colors you can have. In the case of this particular image, only 6 colors on the palette would be taken up, and those 6 colors could be any of 256 different colors. In this case, a red gradient.
Here is a video of these Giygas graphics in action, implemented into Super Mario World as a Mode 7 background:
If I wanted, I could make a scratch ROM that displays all (2^8)^(256*224) images in sequence (which I might).
I could also use a different emulation mode that uses less colors to make the number less huge. I could even make it only happen in a specific 32x32 box on the screen. I haven't done SNES hacking in a long time, and I forget how many colors are in other graphic modes, so I might look up on that later. I mention mode 7 because that's what I'd still know how to off-hand manipulate graphically. (2^8)^(32*32) is 256^(1024) which is still a shit ton.
If one were to run a program to just cycle through all 16,777,216^(2,073,600) images, within this sequence you would eventually see a picture of your face. You would eventually see this very post on screen. You would see every frame of every movie ever made. You would see every frame of movies that haven't been made yet. You would see every pixel of your face, with a green dot starting at 0,0 going to 0,1 going to 1920, 1080. You would see every potential angle that a picture could be taken of your face. You would see every potential picture of a human being (not to mention lots of porn). You would see everything.
In my simple 32x32 window with 256 colors on the SNES, you would see all of the following eventually:
A white image, a black image, an image with one black pixel in the top left corner, an image with it moved over once, twice, all the way to the end. black and white static, the same static with inverted colors, the same static again, but flipped horizontally, ;3, ;o, C, a "Conway's Game of Life" glider, a sprite sheet of Super Mario World boos, the same sheet zoomed in, the same sheet zoomed in so far that it's all just one color, Cook Kirby, and "Cook Megaman".
The smug boo and spy boo are resprites featured in A Super Mario Thing (ASMT) which was a collab I helped produce. The Smug Boo was drawn by Argumentable and Spy Boo drawn by me. Here is an example of them in video: http://youtu.be/BTTSabLFwJI
Not to mention, every frame of that video would eventually appear in iterations of your computer screen. Also, what if you did a similar trick, but with all possible sounds? An SNES also stores sound data in the form of bytes. If I got into SPC-Assembly, it's possible. It'd probably be much, much huger than all possible images.
Even if I had an 8x8 sized space, that's still (2^8)^(8*8) which is astronomically huge. Even if I restrict it to (2^1)^(8*8) which means it's only black and white, that's still 2^64 or 18,446,744,073,709,551,616. (18 quintillion, 446 quadrillioin, 744 trillion, 73 billiion, 709 million, 551 thousand, and 616 different images.)
At a constant 60fps (frames/images per second) on my emulator, it would take 5,209,497,168,964,272 hours to go through every black and white permutation of an 8*8 space. That's 594,284,413,526 years. My computer would probably break down before that happens. Our solar system will be gone by then.
Oh, did I mention, all the basic data for image display in a Super Mario World rom only takes up 512 bytes of space, thanks to the compression and coding it uses.
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Now just stopping here, you have a pretty amazing concept. It'd be pretty cool if someone were doing this with a super computer right now or something. But let's take it further. Think about it, what does the fact that I was able to calculate 2^(49,766,400) as the total possible images you could show on my monitor show? I almost forgot to inlude this half of the post due to short term memory loss while typing the first half. I doubt most people would think to take it this far either. And just because I want to see if this post gets blatantly copy pasted somewhere else, I'm going to type "Diji" right here. Can't wait.
It means that the total amount is finite. Even though every picture you could think of far exceeds what you can image, it is finite. The maximum number of possible images is limited.
At least in our universe. The same idea so far can apply to http://www.hackforums.net/showthread.php?tid=3281155.
Now looking back at my infinity thread, I proposed that within our universe, infinity is impossible.
Planck length is proposed as the shortest possible length. Many of Planck's units are proposed to be the smallest "possible" units of things such as time, or energy.
If you look at a pixel on your computer screen, what is the length of that pixel? You might say, "1 pixel by 1 pixel right?" Wrong. One pixel is 0.264583333mm (millimeters). At least when calculated here. It could vary a bit depending on how big the light itself is for your "pixel".
So that's the length of a pixel. The area would then be 0.264583333^2 millimeters squared. Well, squaring a decimal comes out to 0.07 which is less than the length, so I'm not sure how you would correctly calculate that or if that's supposed to make sense somehow, decimal squaring has always been a weird thing to me. To make this simpler, the length of a pixel is 264.583333 micrometers which makes the area of a pixel 70004.340101388889 micrometers^2. A bit easier to understand right? So the smallest unit of my monitor (a pixel) has that size.
What if we apply that to the smallest unit of our universe? A planck unit, with a length of 1 planck length (1.616199(97)×10^−35 meters which is about 10^-20 times diameter of a proton), and an area of 1 planck length squared.
Looking back at my monitor, there was a finite amount of pixels (1920x1080). There was a finite amount of possible colors. There have been proposed measurements of the total number of atoms in the observable universe (I forget who's number it was, but in any case I remember hearing that people don't take it seriously). Let's just assume for now that the number of atoms in the universe actually is finite. We now have a measurement for the size of the smallest possible units in the universe (planck units) just like we had a measurement of the smallest possible units on a monitor (pixels).
The real universe, however is 3D. Instead of a 2D monitor (x*y), our universe is x*y*z.
I was able to represent a pixel as being the smallest unit on a monitor. I then broke it down to real life by measuring it in units smaller than a pixel, in terms of micrometers. I also gave a break down of the smallest units of the universe as planck units. One important thing I mentioned is that a planck length is many, many times smaller than the diameter of a proton. Throughout history, atoms were once known to be the smallest possible particle in existence. Then protons, neutrons, and electrons were found to be smaller. Then quarks, and now string theory. So, what if our planck unit were the small parts of our strings? Our smallest "pixels".
Based on this, the total possible "configurations" of our universe is finite.
What if I had a super computer, that could calculate its own inner particles in a 3 dimension scale? Perhaps then we could emulate every possible "still-image" of our universe... Not that just going through every 2D image could show us pictures of it already. Of course, this also points out a hole in the idea of exact simulation of reality. A computer composed of particles wouldn't be able to exactly simulate its own particles, nor would a computer within that simulation. When you record the output screen of the same camera you're recording from, you get the cool loop of screens inside screens inside screens. (Funny, I couldn't think of search terms to find a video of this on Youtube). But really, eventually the screens so far in are blurry or dark and are definitely smaller than the outer one (perhaps convex/concave lens would change that). This is why you wouldn't completely be able to simulate reality, and why simulating the human brain would take an extremely huge super computer. (Thank you, Mihiro, for the vid link).
At this point, I highly suggest reading SCP-1190 - Universal Simulator.
Remember how a Super Mario World rom only took up 512 bytes of space? There's an outer entity that can read the data on both how it runs and the graphical data (and musical data). It would be your Super Nintendo, or emulator. Real life...? Think about all the equations scientists find in physics to calculate how things move in relation to each other.
At this point, I also suggest reading SCP-1696 - Dr. Wondertainment’s Little Big-Banger™.
Also of interest: SCP-536 - Physical Law Testing Chamber
If you are familiar with Conway's Game of Life, there is more to elaborate on. Let's say you are running Conway's Game of Life in a 32x32 screen with a block in a middle of the screen. Because of the rules imposed on possible interactions of black pixels, there is only one image possible on the screen. If you place a glider on screen, the only possible images of that "universe" are the separate images of the glider going from one end of the screen to the other. This assumes a closed interval however. What if you had an infinity of pixels for the glider to run across? Then you have an infinite amount of possible images. But back to a closed 32x32 area. Based on your input, there is a finite amount of images, and no other images could have possibly occured. I don't know how to calculate the number of images you can produced in a Conway game of life based off of your input, but the lesson gives interesting implications about our own universe.
As shown in the Wikipedia article, there are other derivations of the Game of Life. Shown on the wiki was one featuring hexagonal cells instead of quadrilateral ones, with more colors than just black and white too. Our own universe could be a much, much more complicated version of Conway's Game of Life.
Here is a video relevant to a common idea I and many others have of the comparison of galaxies to neural clusters and the comparison of solar systems to old models of the atom.
Considering hashlife, perhaps one could make a "Game of Life" for reality and find out what happens at a certain time, just like in the Universal Simulator.
Going back to the idea of a program that steps through every possible image based on an amount of colors and pixels, would there be a reliable way to input a start iteration to see what the image would be like then? Perhaps, like Google image searching in which you can drop in an image file to look for, could you make a program that will try to find the iteration at which your image occurs? For Conway's Game of Life, given an "ending scenario", would there be a finite amount of "starting points" that could have resulted in the finite amount of "ending scenarios"? I think so. It would be a huge amount of starting points and ending scenarios though, considering some ending scenarios can be generated through the same starting points. Of course, there can be no starting points that have different ending scenarios. Another thing in italics to apply to our own universe.
Speaking of a boundless universe, look at the "depth" of a Mandelbrot fractal.
All of this is generated with the same starting algorithm by zooming into smaller parts of its infinite recursion. Mathematically perfect seemingly complex images.
For more information on fractals, see: http://library.thinkquest.org/3288/gnrte1.html and http://en.wikipedia.org/wiki/Mandelbrot_set.
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There is one more step to take with all the information thus far. This one will be brief.
What if those smallest units, parts of our strings, could be combined a different way? We know protons, neutrons, and electrons can combine together to make a specific set of atoms, and specific atoms can combine to make a specific set of molecules. There are some atoms that are impossible combinations, that could never happen. But are protons, neutrons, and electrons the only sub-atomic particles one could make out of our "planck particles"? Or are the combinations that make up protons, neutrons, and electrons the only possible combinations?
What could be made then?
One more SCP article for you, SCP-009 - Red Ice.
