The Odds

There is a slim chance that two people could choose the same set of images and that I might arrange them identically. A very slim chance.

The greatest possibility of that happening is with the smallest number of images - four. But within the full 7x7 grid there are 211,876 possible combinations of four. And each combination of four can be arranged in 24 different 2x2 permutations for a total of 5,085,024 possible arrangements.

Stepping up to nine images arranged 3x3, there are 2,054,455,634 combinations of nine available. Any combination of nine can be arranged 362,880 different ways (who knew?). When you multiply those two numbers you wind up with 745,520,860,465,920 possible arrangements of nine images. 745 trillion is a big number. But it's nothing compared to the numbers you get when calculating the odds with 16 or 25 images or for a full size 7x7 print.

There are 70+ septillion possible arrangements of 16. That's a seven with 25 zeroes behind it. One trillion times one trillion times seventy. Each is 20x20". Estimating that there's 100 drawings per every 2 inches thick, 70 septillion 4x4 arrangements would create a stack of prints twice the area of the continental United States that would reach well past the moon.

9.8e+38. Nine hundred eighty undecillion possible arrangements of 25 images. It looks like this: 980,000,000,000,000,000,000,000,000,000,000,000,000. If each 24x24" print were the size of a grain of sand they would fill the beaches of close to 100 trillion earths.

A novemdecillion is a one with sixty zeroes following it. There are 600 novemdecillion or 6e+62 possible 7x7 arrangements. This is a staggering number, equal to a mass of prints that would fill the Milky Way galaxy four times or a stack of prints that would criss cross the known universe nearly two million septillion times. Essentially a meaningless number.

However, in this instance it does pretty well mean that no two prints will be identical and I think the same could be said for any size set. There is the human element to consider. Certain drawings are bound to be more popular than others and I do have a loose set of unwritten rules by which I arrange them. But I don't believe either of these factors will affect the odds in any measurable way.


Patterns Within Patterns

The clickable pattern pictures on each Choose page were created to give an impression of the near infinite number of possible arrangements as described above. A random dance depending on how fast you click. I hope they succeeded in giving that impression but an impression is all it was or could be. I suppose some sort of random image generator could have been created with the drawings inputted and the generator programmed to choose one and then choose another from the remaining drawings, and another from what's left again and another and another and so on. I think it would have been a bit complicated and pretty expensive to have a bunch of those made. (Plus how long would the pages take to load?) Instead a "clickable movie" was made. Each frame or set of images was created by dragging and dropping the square drawings into a template (similar to how the prints are made). Each click brings you to the next frame in the movie.

This provided an opportunity for some fun for me. I'm going to be dragging and dropping them anyway. Why not make them do something? So that's what I did.

42/4 - For the first one with only four images to work with I think it would have been too obvious so nothing was done. There are simply 13 different sets of four to click through until it starts again.

42/9 - This one is the easiest to notice, not just because it's only nine drawings but because the drawing that moves is the most starkly black and white of the entire set. It starts in the top right corner and rotates counterclockwise from corner to corner as you click. Perhaps you noticed. But did you notice that at the same time, with one frame/click disparity, the four drawings beginning at the north, south east and west positions rotate clockwise once around? Then there's a few random frames to throw you off before it begins again.

42/16 - If you happened to notice the movement in 42/9 you may have looked for something similar on the other pages. Here, in the first frame; from the bottom left corner the drawing slides along the bottom and then up the right side as you click. Beginning with the second frame the bottom left corner drawing goes up the left side and across the top. It's a race where the first one always wins and the second one never quite gets there.

42/25 - My favorite. The center drawing changes each time. The inner layer of eight, around the center drawing, rotate counterclockwise. The outer layer rotates clockwise.

42 - Full Set - The third drawing up from the bottom, in the center, is the apex of a "V" of drawings (one up and one over in both directions repeated until you get to the edges) that travel downward in a straight line as you click. At the same time the drawing top center is the apex of a second "V" that also travels straight down. Very hard to follow since each drawing is pretty tiny on the page but that's what happening every twelve frames. Seems like more than twelve don't you think?