Elevation XI: Uplift Revisited

One of the most important inputs to the erosion model is the tectonic uplift. I've tried a few things with this in the past, and now I'm back again for another crack at it.

The basic idea behind a hex's uplift value is its distance to convergent, transform, and divergent faults. It's difficult to compress this all into a single number, so I played around with the values until I arrived at this, where i and max_i represent the maximum distance from the C/D/T faults:

uplift = (
    0.5 * c/max_c +
    0.1 * t/max_d -
    0.4 * d/max_t + 0.399
)

So every hex will have a relative amount of uplift on a scale of 0 to 1. I do rescale this later so it goes from 0.1 to 1: no uplift means problems like sub-sea elevation terrain that I don't want to have to deal with (thanks, New Orleans).

Fault map; yellow is the highest uplift, blue is highest divergence, and white is a conjunction of all three

This number can then be fed into the erosion model to determine how much the land is rising while water is trying to eat it away. Usually, the tectonic plate wins.

So this gives us the first version of the uplift model. There are a few surprises, where I expected to see higher values, but it turns out that these are in proximity to divergent boundaries which reduce the overall number.

But this is too simple (of course). Plates don't collide like this: they ripple. There's a good approach here on one solution to this. I'll take a different tack, simply using a screening mask to to modify the values. Yet another optimization step! But this is what I will use initially, after much mucking around with different values, where $u_0$ is the initial uplift, $u_f$ is the final uplift, and $a$ is some constant.
\[u_f = \left(u_0 + {2 \sin(a u_0)\over a} + {\cos(a u_0^2) \over a}\right)^3\]

a = 50

Looks ok. Just too smooth. So we'll salt it a bit with some simplex noise:

There's still a significant problem as it relates to the overall terrain, though. There's really only one major mountain range. Everything else is at least half that value. Either 1) this is ok, and just an acceptable outcome of the inputs or 2) I can use gamma correction to modify the map.

But I'll tackle that later.