Doodle Brains

Van Gogh by way of Monkeys



In 7th grade I bought my first CD: Blink-182's Greatest Hits. I started watching American Idol to be able to have something to talk about with a girl I liked. I won a guitar at an amusement park. This is me in 7th grade.

A Young Me

Except it's not really. It's a digital image, made up of pixels, 90,000 of them. Here’s another grid of 90,000 pixels, very much like my yearbook photo.

Pale Blue Dot

Except it's not really much like my yearbook photo, because it's Voyager I's Pale Blue Dot photograph of Earth from 3.7 billion miles away. Exactly one of those 90,000 pixels is planet Earth.

What I'm trying to get at is that these images are simultaneously utterly regular and utterly irreplaceable. They both speak volumes, and yet here they are both just sitting on this no-name website. So what if instead of going to these (literally) astronomical lengths to photograph this breath-taking grid of pixels, what if we did it the other way around: just shook up a frame of pixels until it made something meaningful?

In theory*, there is nothing stopping us from randomizing 90,000 pixels and creating that exact pale blue dot photograph, pixel for pixel, without ever having to send the Voyager into space. We could also create a photorealistic image of you and Caesar shaking hands, or you reading the front page of tomorrow’s New York Times. Not only can we create any picture, we can create every picture. Or, of course, just random noise.

Random Noise

Thomas Lum


Random Noise (2018)

Javascript, Pixi, Macbook Air

You may have realized this is really just a visual variation of the Infinite Monkeys thought experiment, whereby an infinite number of monkeys banging on infinite typewriters after infinite time could, by chance, type out the complete works of Shakespeare, verbatim.

But, even if we never generate the plays of Shakespeare, or the art of Van Gogh, what remains beautiful about those tweets and the portrait of noise above is that they are all discrete and unique. If you were to generate another random 90,000 pixels, you would have just as likely a chance of creating the pale blue dot photo as you would that particular random array of pixels. This is the philosophy behind the revolutionary, historic, critically aclaimed 1 Monkey App. It does the job of one of the infinite monkeys, it generates a random portrait, and for proof of randomness: a “title” that anyone can enter on their own app to re-create your work.

1 Monkey
Embrace Randomness
Find Meaning
What will you discover?

*...Did you follow the asterisk down? Cool, because the secret to this thought experiment is that in actuality, the protagonist isn't really the power of randomness.

It's Not Easy Being Random

Scientists and experimental artists, being who they are, realized they had to one-up philosophy and actually try the Infinite Monkeys thought experiment... with real monkeys on a real typewriter, the final, published work of which you can find right here. As you'd expect, the results are... less than Shakespearean.

One reason for that is because Monkeys aren't a good source of randomness. And this is to be expected, even humans aren't very good at being random. Our thoughts don't come from a vacuum, but from our previous train of thought and our environment, which is why when I ask you to not think of a purple elephant, it’s very hard not to.

Even computers, who are very often relied on to be random, are only doing a really, really good job at faking randomness. Computers are, after all, deterministic machines by design, which is why random number generation is often more properly called Pseudo Random Number Generation (PRNG). Essentially, if you take a hard to guess number, like the exact current time in milliseconds, and perform a really complicated jumbling function on it, you can get a pretty random looking, hard to predict number. If you want to learn more about randomness (otherwise known as stochasticity), I highly recommend this stupendous radiolab episode. But just like me in 7th grade, the real problem isn’t about how random we can be: even if we had a perfectly random machine, there is a stronger current we are pushing against.

Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really Really
Big Numbers

A single pixel is made up of 3 tiny lights: a red one, a green one, and a blue one. Much like mixing base paints to make new colors, mixing the brightness of these three lights allows pixels to blend what our eyes see as a single distinct color. Each color light can have a brightness value from 0 to 255, meaning a single pixel can produce a total of 16,777,216 (2563) different colors.

Color #








If you were curious to see this animation all the way through, just make sure you have roughly 170 free hours. But if you don’t have the time, David Naylor was kind enough to create the entire palette of your monitor in one single, very big image.

Just like the yearbook photo and Pale Blue Dot above, the dimensions of the web version of the 1 Monkey app are 300 x 300, totaling 90,000 pixels. What this means is that the number of images that are possible in 1 Monkey's tiny frame are 16,777,21690,000, or about 10648,370. This is a truly impossible to comprehend number. Astronomical numbers don't even put a dent into it. 10648,288 universes of atoms fit into this number. And an astounding thing is that all it takes to make that number impossibly bigger is to add one more pixel to the frame, essentially 16-billion-ifying it once more.

But, a number that’s infinitely larger than even that number is, of course, infinity: the important crux of the infinite monkey theorem. Even if the chance for a pixel perfect Pale Blue Dot is 1 ⁄ (16,777,21690,000), given infinite time, that exact roll of the dice must happen. Shakespeare’s texts are only proven to be possible to generate, not probable.

But… why? What is it that makes Shakespeare different than monkey gibberish (if you ask anyone not forced to read it for school)? These facts alone don’t preclude the ability to generate Starry Night on our first try, yet if you give 1 Monkey a shot you’ll find that your results are more… Pollock than Van Gogh. So what makes our random portrait so different than the pale blue dot? Is the protagonist of our story something else? Again??

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.

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.


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

By way of Monkeys

Consider an image that is the paragon of order. A perfectly blank, 300 by 300 image.

This image scores an A+ on our metrics of color and spatial order, but it’s not… meaningful. In fact, it’s just about as meaningless as our random portrait. So, order alone isn’t sufficient for meaning.

This is doubly strange when we consider the fact that you’ve already seen this image before: this Big Green Square is actually the eponymous Pale Blue Dot in the photograph taken by the Voyager. And when in that context, it is almost the entire meaning of that photograph. But how can a single pixel represent the entire Earth? If that is the case, is our picture of random noise not just 90,000 multi-colored Earths?

As ludicrous as that notion sounds, it’s not that far from the truth. Something you might’ve already noticed is that 1 Monkey portraits don't feel entirely meaningless. While it may fail as an Obama portrait generator, 1 Monkey is really good at making images that seem to almost look like ephemerally meaningful images, like finding shapes in clouds, or staring into a Rorschach blot. This well studied phenomena we perform without thinking is known as Pareidolia, an effect where, even from basic or nonsensical stimuli, the brain perceives meaningful images.

And this to me is the beautiful twist of the 1 Monkey app: its designed purpose is to create meaningful images, and while it horrifically fails by many an objective measure, in a subjective manner it will always win because your brain is a meaning machine.

Well, that’s the end of the line folks! We hit that logical conclusion: cognition and consciousness. Pack it up! Ain’t nothing out there for science in that swamp. Don’t you see? The magic was in YOU all along!

Based on how long of an article this has turned into, I’m almost willing to call it a day and believe that. So instead we’ll compromise. We’re about to dig into some of the biggest cans of worms looking for answers that chances are, we might not find, or we may find in a way or form we weren’t expecting. We’re gonna try and dig into entropy, cognition, stygmergy (my personal favorite), information theory, and… honestly I’m fooling myself if I think I know ahead of time what else. And because of what I want it to be, this article probably won't end up being the next doodle brain.

But until then I’ll leave y’all with a question that always comes back to my head. I call it the three lines problem: What is it that makes the first and second line boring, but the last line meaningful?

You already know the answer now is not the images themselves, but you. The next question in the queue is then: what makes you so different?


  • If we wanted to make an app that generated meaning better than 1 Monkey, a good idea would be for it to learn from humans, instead of working randomly. What might that look like? Maybe something like this.
  • If you're curious, you can check out the charts used in this piece in more detail over at Plotly.
  • You can play around with 1 Monkey as a standalone webapp, as well as the mobile app version, with a different resolution and aspect ratio. You can also get just the color counter.
  • I apologize that the mobile version doesn't have a 300 x 300 version, I couldn't get react native to use Pixi, so the performance I was getting (with my brief knowledge of react native) just couldn't take that size.
  • If you want to see more of the full color spectrum in action, check out, a website devoted to artwork made using all 16 million RGB colors.
  • If you want to see a famously impossibly big number, check out Numberphile's great video on Graham's Number.
  • I'm going to have to mention that Radio Lab Episode on Stochasticity one more time because honestly it's fantastic, and I had to force myself to stay on topic and not dive into ten more pages of thoughts on Randomness. Not gonna lie, this episode along with a bunch of other Radio Lab episodes pushed me into my Comp Sci & Cog Sci majors.
  • I'm going to have to mention that Radio Lab Episode on Stochasticity one more time because honestly it's fantastic, and I had to force myself to stay on topic and not dive into ten more pages of thoughts on Randomness. Not gonna lie, this episode along with a bunch of other Radio Lab episodes pushed me into my Comp Sci & Cog Sci majors.
  • And as always, this app was made using the awesome PixiJS!