I was screwing around with graphs for no particular reason when I found a very interesting graph on my emulator.

Window:


EDIT:
Enhanced version:

Cool. I'll try and come up with an explanation ASAP, but I'm tired!
Edit:
It's basically just a hyper-compressed sine wave, but the emulator/calculator can't handle it, so it picks which pixels have the highest density of points in them, and draws it. This is only my guess, but it makes sense to me...

I wrestled with the code, and I managed to get a version on my 84+cse emulator. I figured out that converting from previously 1x1 pixels/point to 3x3 pixels/point was not too difficult, and similar transformations could be manipulated through algorithms. I don't see any practical purpose besides maybe maze generation, but it does make some interesting characters.

Result:

I got a similar result to happen on my CE.

And it is not of any use for maze generation. Try it again, but this time do [Zoom][0] (ZoomFit) and you will see it is a simple (but elegant) repeating pattern.

It is very cool, but when calculated by hand (omg this took me like an hour, and I probably screwed up) it does not give the same result.

iPhoenix: Not quite. Think about how the calculator draws graphs in Function mode. For each column of the graph screen (because deltaX is always the step from one pixel column to the next one), it plugs that X value into your equation(s) and produces a Y value; it then turns the pixel at that (X, Y) on. When you're in parametric mode, there's nothing that forces it to only sample one Y value per column of pixels. Because you have effectively made it sample multiple X values that map to each column, since the screen is so low resolution, you end up with it graphing several (X, Y) points in the graph that appear to be in the same column (even though their X values are slightly different). Makes sense?

I was thinking that if this function was modified, the screen could be filled with maze-like patterns. I'd probably use a worm to do the same job though. Either way, it did create an alien-looking sequence of characters.

Yeah. If I was to create a maze gen algorithm, I would create a bunch of square segments that have openings (to lead into other segments) on all of the sides. I would then fill a screen with a bunch of randomly selected ones, and BAM, maze!

Because of the way this (currently) works, you'll always get repeating patterns. You could throw some randomness into the mix and see how that affects the output, though!