Starting on Tectonics

This turned out to be harder than I thought. There's some publicly accessible information about simple vector math for fault lines, but not a ton, and of course, none of it is applicable to my particular map projection. So I had to piece together what I could. In addition, while the meeting of 4 plates at a point is technically possible, it almost never occurs, so I had to ensure while redrawing that plates only met at boundaries or triple junctions.

Thankfully, the map projection allows me to ignore the Euler vectors, which is nice, but then I have to wrap my head around correcting for all of the other transformations.

I also did all this in a really hard, really janky fashion. It's clever in that special way that avoids doing it the right way. Rather than saving the position/motion of plates at a single point, I encoded the vector in the colors of the lines themselves. This is a technique that I've been using a lot in this work, but usually in a monochromatic form. Essentially, each RGB code is a 3-channel, 256 resolution carrier for information. All I have to hardcode is those colors, write a bit of code to translate it back into motion vectors, and ta-da!

The math is a bit complex at first but eventually I figured it out to a point where it works. The important vectors are $\mathbf{d}$, which is just the relative motion of the top plate A to the bottom plate B. If this vector is pointing up, the fault is moving away from the bottom plate faster than it's moving towards it, and it's a divergent boundary (so the figure should actually show blue, not red). If $|\delta|\leq35^\circ$, the plates are moving more or less parallel to the plate (this value is arbitrary, 35 seemed good enough for what I was working with), and it's a transform boundary. I then scale the strength of divergence or convergence by the vector rejection $\mathbf{d}_{\perp\mathbf{f}}$, and if it's a transform, by the vector projection $\mathbf{d}_{\parallel\mathbf{f}}$.

There are still some zones that I need to check: R/S and I/J look odd. Then again, sometimes the combination of vectors make for interesting results. It's a neat bit of code, but nothing groundbreaking (I'll show myself out).

Next: make these lines dirty and see what happens!