Order Up!

One answer is that photographs, books, paintings, all have order, rather than randomness. I used Pollock a second ago as a stand-in for something random, but truthfully even Pollock's paintings have significantly more order than our random portraits. Let’s take a look at three images that we can clearly line up from least to most order.

Leftmost we have our random noise portrait from earlier, center we have a section from Pollock’s Convergence, and rightmost we have a portrait of Barrack Obama. Just by glancing at these images we can see order increases from left to right. But we didn’t get a CS degree so we could deduce things with our eyeballs. We need to think of how to measure order, and then create a compelling visualization to deduce with our eyeballs.

The first row of visualizations below samples pixels from these images and places them on a z axis (coming towards you) according to the pixel’s brightness. What this does is highlight the shapes that are found in the image: patches of space that have a congruent brightness. This brings out the spatial order of the image.

The second visualization samples the colors used in these images, and shows their distribution in 3D space, where the axes are the amount of red, green, and blue. While this doesn’t speak to spatial order, it does show the range of variance of colors, the chromatic order, in a sense.

Reset ↩ Spin 🔄 Reset ↩ Spin 🔄

As you can see, Obama clearly wins out in the measure of spatial order. The white background, as well as his suit, stand in sharp, distinct shapes. Even the gradients of light on his face are near each other as they slope into the z axis. Our two works of art on the other hand are pretty similarly chaotic when it comes to spatial order. There are no easily discernable patches of bright or dark shapes that catch the eye. However, when we look at the color cubes, we see that while our random noise fills the entire space, the colors used by Pollock are much more ordered and limited, and even look a lot like the palette of Obama’s portrait.

So it seems that 1 Monkey often generates random, chaotic images, unlike more ordered, meaningful images. To put a cold hard number to this intuition, let’s consider the possibility that we generate a 1 Monkey portrait that doesn’t have any stark green in it, just as Obama and our Pollock do not. We’ll consider a green to be any color where the green value is 100 greater than the red or blue value. This allows colors like white, with rgb(255,255,255) to be not registered as green, despite having a lot of green light. To calculate how many greens are in this range, we can think of how many possible reds and blue values there are for each Green value from 100 to 255.

Green = 100



[1 Possible Value, 0]2

= 1 Green = 101



[2 Possible Values, 0-1]2

= 4 Green = 102



[3 Possible Values, 0-2]2

= 9

Which we can extrapolate to be

Or 1,277,666 greens. So, what are the chances of creating a 300 x 300 image with none of these distinct greens? About 1 in 103097. Or picking the right atom in 103015 universes. Just to get an image that doesn’t have green in it. Not an image that looks like Obama, or has any discernable shapes, just an image that doesn’t have green. So, meaningful images have order, which is inherently the opposite of randomness, which is what we are using to generate our images. Dice are meant to be unbiased, but what we are waiting for are the few moments they appear perfectly biased and meaningful. And 1 Monkey is a first-hand example that there are more chaotic possibilities than there are ordered ones.

...except...

well... okay, there’s one more element to this equation, the real real protagonist to our story.