Pick a set of directions on a grid. This is your pattern. Weens (weeds) start at the center and spread. Every day, each ween copies itself in every direction you chose. Take a note of the sequence for a few days and you'll quickly notice the count starts following a clean quadratic: W(n) = an² + bn + c, where n is the day.

The way you actually find this formula is through second differences. Take the day-to-day growth, then take the differences of those: the rate of change of the rate of change. Most patterns will be erratic early on, with an erpe (erratic period) of length n. Once it's been flat for several days in a row, you can fit a, b, and c exactly. That moment is what stabilized at n = ... marks.

Once a pattern reaches a constant second difference value, dividing this by two gives a, and it has a clean geometric formula: a = erea ÷ prick. Erea (shown on the app) is twice the extreme area — the tightest polygon you can draw around all your chosen directions. Prick accounts for gaps: when your vectors share a common divisor, the grid they generate is coarser than the full integer lattice, and prick measures that.

b is the open problem. We know it's connected to the inner structure of your pattern and to w — the number of vectors you placed. There's a proven formula for certain cases, and the rest is still being worked out. That's what this tool is for.

We haven't done that much looking into c yet. What we're guessing now is that it captures the irregular early period before growth settles into its quadratic period.