== Modes == Mode 0: manual mode In mode 0, you have control of all values. Press UP / DOWN arrow keys (or use scroll wheel) to increase or decrease the number of points respectively. Similarly, you can control the factor using LEFT / RIGHT arrows. Mode 1: Point count is mapped to your mouse's x-value. Count goes from 20 to 220. You can still control the factor manually. Mode 2: Factor is mapped to your mouse's y-value. It is rounded to the nearest 0.05. The range is from 0 to 8. You can control the point count with up / down, just as with mode 1. Mode 3: Auto mode. This is the combination of mode 1 and 2. You can press LEFT MOUSE to centre the graph.
This is a program which draws times tables. You probably know your 1, 2, 3, ... 12 times tables. But do you know what they might look like on a graph? Well, this is one way they can be mapped. Basically: each point has a number. The first point is 0. The "factor" is the times-table being graphed. Each point first gets its address, multiplies it by the factor, and then goes to that point on the circle. The numbers loop around, meaning that instead of 4*3 going to point 12 (when there are only 10 points), it goes to point 2. The formula for what each point is mapped to is this: i --> (i * factor) mod (points) Where "mod" is the remainder function (modulo) and "points" is the number of points. == Interesting observations == Perhaps they aren't really all that interesting. But here are some. The apparent shape factor is equal to the actual factor minus the number of points minus 1; this means that if you have a factor of 28 and 26 points, the shape appears to be a cardioid (factor 2). For factor 29 (but still 26 points), the shape is a nephroid (factor 3). There are more, but I don't have time to find them properly. Remind me if I haven't done it soon.
