The Super-Man logo was interesting enough to put on a calculator, but I want something bigger. The obvious next step is to create a lidless eye, wreathed in flame that can watch everything that goes on in the world. I am going to create the Eye of Sauron.

The tower should only be about three functions: one for each of the two spikes holding the eye up, and the last one for the bottom part of the tower. The eye itself will be more complicated. I could create two sine waves and have the function be everything in between, but that would be lame. I want just one, cool function that takes care of the fiery part. Luckily, I found a quirk in the calculator that allows me to do that.

The function y=10sin(99999999x) (that’s 8 9’s) yields something close to two eyeballs when my calculator window is at the default setting. I cannot say for sure why this happens. My best guess is that when the frequency of this wave is so large yet so close to a power of 10, each step (the next point that the calculator plots) appears to move slightly along a wave. If I took the absolute value of this function, it would just look like a large sine wave. However, every step changes the sign of the y value, creating the nearly vertical segments.

I prefer the left eyeball for the end product, so I am going to multiply the whole function by sqrt(-x)/sqrt(-x) to get rid of the positive x values. I am multiplying the equivalent of one, so I should not be affecting the actual values. However, as soon as the calculator detects an imaginary number while it graphs, it panics and says “ERROR.” I am using my calculator’s stupidity to my advantage.

To make the pupil, I just need to put in a horizontal line or sine wave in the middle of the eye. After this, I need to make functions that shade below a given line. However, just creating the shade functions make the tower look weird.

I need to end the left function before the interfere with the right function. Otherwise, the tower will just look stupid. If I put in sqrt(-x)/sqrt(-x) for both of these functions, then everything will come out neat.