Is it possible to automatically generate images out of the functions in Image Functions? The answer is yes! It is possible with genetic programming. Let's explore this.

Suppose the image we're trying to match is this picture of Charles Darwin:

Here's how it works: We first create a population of randomly-generated functions. Then we evaluate each of these functions and see how close they match the image above. We take the best ones out of this population, and create a bunch of replicas of them with a few differences (mutations) to create a new population. This process is repeated for each generation of the population until one finally matches close enough to the original image, or until we give up. I'm glossing over a lot of details, but there are plenty of tutorials on genetic programming to get a better understanding of how it works.

Unfortunately, trying to match a single function to try to generate the entire image doesn't work so well, so we had to give up. Here's the best result achieved so far, on a smaller version of the image:

The function for this failure of an image can be seen here. It's rather large (too big to put into the web app, so don't even try).

If we split the image into a 10x10 grid, however, and try to match each piece of the grid to their respective piece of the original image, we get a much better result.

The functions that produce this image can be seen here. If you implemented the same version of the renderer (or download mine, when I release it), you should be able to plug these functions in to generate the exact same image, at arbitrary resolution.

Here's a video of the algorithm's progress with one frame per generation. It gets pretty close fairly early, and slowly refines itself.

You may wonder why we would want to do this. Well, take this image for example. Consider the fact that the image, in .jpg format, is almost 40,000 bytes in size. However, look at its representation on the bottom - 223 characters long. That's just 223 bytes, and that's not even counting the fact that you can compress the text itself. Probably down to about 40 bytes. There is great potential for compression here, if we could just figure out how to do it for general images!

What's next? Well, the grid thing seems to work fairly well, but the image still lacks some detail. We probably want to implement a quad-tree algorithm that will cut the image into a 4x4 grid, try to match the pieces, and for those that didn't match well enough cut them down even further. This should allow the algorithm to automatically focus in on noisy parts of the image.

Oh, and yes. Eventually we will get this going with video. And audio. That will be pretty awesome.