Many scientists agree that the universe got it's start with a bang. One that was so large it created all the mass and energy in the universe. If this ball of energy was PERFECTLY SYMMETRICAL, we would not see any galaxies, stars, or planets. The universe would be a homogenous cloud of energy, devoid of anything of interest. There would be no points of light in the night sky, no ground to stand upon, no life of any kind. Nature knew from her start interesting stuff is born from chaos with rules.
Chaos by itself, of course, wouldn't produce any meaningful universe either. But, chaos never appears by itself, not in all the universe! There is always some set of rules working on it, gravity, radiation, presure, friction, and chemistry are all at work regulating chaos everywhere, always. Even in theoretical mathematics, true chaos, seems impossible to achieve.
Computers can process nearly any kind of information. Computers can employ algorithms to process numbers, letters, audio, pictures, even video. Software is a kind of data that describes, in minute detail, how to process data, the instructions, the algorithm. Hardware is the rules the software must follow in order to function correctly.
But what about chaos. Can computers make chaos? I am not asking about the kind of chaos that happens when you loose your computer based photo album from last Christmas. I mean numerical chaos, a list of numbers that doesn’t seem to follow any rules. Can computers make a list of random numbers?
A fair question, considering computers work with bits and math. A bit can be one or zero, no middle ground. A computer containing a finite number of bits can't even exactly represent irrational numbers, like pi or square root of two... Therefore, "Computers can not generate truly random numbers." But, computers can employ complex mathematical formulas and algorithms on the numbers, making the next number very difficult to predict.
A simple method for generating a disordered list of numbers is a shift register with exclusive-or feedback. Two or more bits from the shift register are combined becoming the next input bit. This is often how computers make disordered lists of numbers. Software that makes information unreadable to anyone without a key uses more complex methods like DES, RC4, or MD5.
What can pseudo random numbers be used for? If they are so hard to predict, how can you use them to do anything meaningful? If you apply rules on the random numbers they can be very creative. Below is an example.
The maze above, can be generated by planting a "Seed" (a white pixel somewhere within the black) and then building hallways into the available black area. The random numbers in this process select the location of the seed, intersections, and direction of the hallways. Some computer programmers have a fear that the algorithm might never finish; but, if you count the maze's available space and there is none, it is finished. Furthermore, even when potential intersections are chosen randomly within the boarder of the rectangle; it will finish, because, the area is finite.
This image is created using chaos as well. Rectangles, with random dimensions and placement, having a yellow interior and cyan walls, are drawn over each other. After a predetermined number of rooms are drawn, the space remaining is left light green. The dark blue squares are doorways. To ensure every point is accessible, a procedure like the black and white maze is utilized. A seed area is selected randomly. The area is filled with a flag. The flag indicates it has been selected. A search across the whole image is made to find cyan walls that have the flag on one side and no flag on the opposite side. A randomly selected cyan wall, found to have a flag on one side but not the other, has a door placed into it. The area that does not have the flag in it is filled with the flag. The last three sentences are repeated until there are no more cyan wall that have the flag on one side and no flag on the opposite side.
The Color Clouds, above, looks a great deal more organic then the other two. You could be asking, "How can chaos make an image like that?" Imagine four pixels in a two by two area. Each pixel has three components, red, green, and blue. Each component has a range from 0 to 255. Every component in all four pixels gets a random number between 0 and 255. Both dimensions of the four pixel image are doubled making the image 4 by 4 pixels, or a 16 pixel square. In a random sequence, each of the 16 pixels is averaged with the neighboring pixel's components. To the averaged components a random number between -127 and 127 is added. If the resulting number is outside the range 0 to 255 it gets clipped to inside the range. The process repeats, double dimensions, average neighbors, add a number; but this time the random number is half the range -63 to 63. Again and again each time doubling the dimensions, averaging each pixels neighbors, and adding half the range of the previous run, until the image is the desired size.
OK, that's in a computer; how does this concept apply to reality?
If you had a barrel of marbles, on the left side red and on the right side white, and shook them vigorously until they were all mixed up; how much longer will you have to shake the barrel until the red marbles are on the left and white marbles on the right? Obviously, you are going to be there an impossibly long time!
That would be a fine metaphor for a universe made completely of just red and white marbles. Allow me to expand this argument just a little... Instead of red and white marbles, lets make them steel and glass, steel on the left and glass on the right. One more thing, we bring the barrel into the Earth's gravity a few hundred feet above sea level. Begin shaking...
Steel is much more dense then glass. You would expect the steel marbles to all find there way to the bottom. That is exactly what happens.
Something unexpected might be more convincing.
Get a bunch of Lego Building Blocks and a large clear plastic container. Select just the full height 2 by 4 blocks and be sure each block is separated and put them into the large plastic container. When the container is nearly full, seal it, and begin shaking the container. After about five minutes, you will notice many of the blocks have joined together in a very specific way.
Carbon 60 is a molecular sphere of carbon, 60 Carbon atoms chemically bonded in such a way that they form a sphere. "I've had some chemistry courses, love PBS, and I want to show off." Did you know they first found C60 in the interstellar dust of space?
You might say, "That's impossible! Nature can't make highly ordered molecules like that."
I did some research on the PBS web site and found an article on Scientific America specifically about C60. The article stated, "The easiest way to make C60 is to cool Carbon gas in the presents of Helium. A Helium atom has the perfect size to fit just inside the C60 molecule. This explains why Carbon 60 and other Fullerenes are so common in interstellar dust." — Paraphrase
Some people believe chaos can't do anything creative. These same people would have you believe, evolution is impossible; and, countless random events cannot create anything of value or beauty. If you are one of those people, I invite you to consider, the black and white maze was created with a few hundred random numbers, the rooms were created with a few thousand random numbers, and the Color Clouds were created with under a million random numbers.