Stochastic Geomophical Transport for Terrain Erosion Simulation
One major way to model terrain has been through simulating erosion: how the rock weathers away is a big component of the vibe of the landscape on a geological scale. But there's a couple of components to that: both the erosion itself and also where that material goes afterwards. In short, this new simulation from Nicholas McDonald and Guillaume Cordonnier handles both mountains and rivers.
(Another major way, of course, is Perlin Noise and related approaches, which eschew teleological realism but gain other benefits.)
The idea here is momentum conversation: using a new particle-based algorithm (which can be combined with other geological processes, like tectonics and wind direction) it simulates geomorphological transport, which operates over geological time, taking advantage of the difference in timescales: over the course of geologic time, a river is basically instantaneous.
This makes it very flexible for mixing "a wide variety of phenomena" as they say: in the paper they describe the potential for things like dunes, coastal erosion, floods, rockfalls, varying erosion weights. I particularly like how effective it is at effects like braided rivers and river deltas, which are very common in nature but often overlooked on procedurally-generated maps.
On the other hand, if the erosion is fast (individual rockslides) or transport is slow (glaciers) that breaks the assumption and it won't be as accurate at modeling it.
I think the reason that I'm personally drawn toward this algorithm is because it has a history that is naturally embedded in it.
You don't necessarily need to replicate the exact phenomena that was involved in creating something to get a good result. Much of games and simulation is about picking the right abstraction to get the right feel, regardless of how you get there. It's often the better call, to get the right poetry instead of the exhaustively correct metric. But one benefit that you do get replicate the physical causative process to try to simulate the physical effects of water, wind, and time is that it comes with a built-in sense of history.
Simulation creates its own history. In looking at the terrains produced through this method, you can see the paths of historical rivers, the canyons carved out over millennia and eons. All the details that humans find hard to capture just because of the sheer amount of subtle detail that builds up in tiny ways.
