Question

I was reading through this interesting post about using JavaScript to generate an image of a rose. However, I’m a bit confused, as this article claims that the author used monte carlo methods to reduce the code size.

It’s my understanding that the author was using monte carlo methods to do something like GIF interlacing, so that the image would appear to load more quickly. Have I missed something?

Answer 1

The Monte-Carlo (MC) method used by the author has nothing to do with the resulting image file type, it has everything to do with how the image was generated in the first place. Since the point of JS1K is to write compact code, the author defines the rose by mathematical forms that are to be filled in with tiny dots (so they look like a solid image) by a basic render.

How do you fill those forms in? One method is to sample the surface uniformly, that is over a set interval, place a dot. As @Jordan quoted, it will work if and only if the interval is set correctly. Make it to small it takes to long; make it to large, the image is patchwork. However you can bypass the whole problem by sampling over the surface randomly. This is where the MC method comes in.

I’ve seen this confusion over MC before, since it is often thought of as a tool for numerical simulation. While widely used as such, the core idea is to randomly sample an interval with a bias that weights each step accordingly (dependent on the problem). For example, a physics simulation might have a weight of e^(-E/kT), whereas a numerical integrator might use a weight proportional to the derivative at the sample point. The wikipeida entry (and the refs. therein) are a good starting place for a more detail.

You can think of the complete rose as a function that is fully computed. As the MC algorithm runs, it samples this function while it converges onto the correct answer.