January 29, 2020

Elevation XV: From Square One

I wanted to take a break from prehistory stuff while I read up on hunter-gatherer sociology. I decided to revisit terrain generation.

My current terrain was created by drawing continents I liked, loosely matching them with tectonics, generating uplift values from that, then performing hydraulic erosion until I liked it. I'm still not ready to move into tectonic simulation, but I wanted some landforms that more closely mimicked the plates I'd drawn. I also took the opportunity to clean up the hydraulic erosion code.

It turns out, perhaps predictably, that the tectonic input map is perhaps the most important variable of all.
 Fault map, showing convergent influence in red (with transform in green and divergent in blue)
I experimented with a variety of drop-off functions (Gaussians, other exponentials) to find a good way to find the closest fault (or most influential fault, by strength) to a given hex. This took a really long time, because I had to iterate over ~2000 fault hexes for each of the ~250000 world hexes. Some Poisson sampling helped, but even then, my uplift map ends up with circular ripples.
 Uplift map: the Poisson disks are particularly obvious along the convergent equatorial fault
Where the uplift map is too patterned, the landforms tend to be also. So I tried adding in various kinds of warped and ridged noise to try and mix up those forms. One big problem with using noise of any kind is that it looks much too uniform at all scales. A quick look at Earth's coastline reveals a variety of types of "noisy" coastline, some smooth, some rough. So any kind of realistic noise function will need to approximate this variety. The hydraulic erosion discussed below can help with this. However, I still think more work is needed to obtain a better fault/uplift map from the input tectonics. One on-going issue is that the basic tectonic distribution persists from the time when I did most of my work by direct sketching. Maybe next week I'll work a bit on a generated (or at least computed) fault map to add more variety.

There are four basic processes which can alter the altitude of a hex: d$u$, the uplift of the plate; d$e$, the removal through erosion; d$s$, the deposition of transported sediment (from eroded material); d$c$, coastal erosion.

Although I had used a simplified version of this model before, I hadn't considered some practical limits:
• A hex will stop eroding once it is completely "ground down," that is, its height is equal to the height of the hex to which it drains. At this point, water no longer flows. Hexes under sea-level do not erode with the same mechanism. For now, I've turned it off, but a possible alternative is a constant rate of erosion. As always, erosion rate is determined by how many hexes drain into the target.
• On the other end, once a hex has been completely filled with sediment, it won't accept any more drainage. This one is a bit more complicated: I compare the height of the hex to the height of all other options that the source hex could use. Once the sediment makes the hex no longer the lowest of all the source's neighbors, drainage will instead flow into the new target. So it might not necessarily reach the height of the source.
• Coastal erosion stops once the hex has been eroded under sea level. The erosion rate is faster the more sides are exposed to the ocean. I think it might be interesting to continue to transport and deposit that sediment elsewhere, but that would require the current model to run every iteration.
 The coastlines look pretty good but the overall landforms indicate I need to do more work with tectonics and uplift