The erosion is not physically correct, but gives the look of an eroded terrain.
The eroded terrain is on top, the medium eroded terrain is in the middle, the original is at the thrid.
The bottom-most is the result from computing a 2048x2048 map.
The method simulates 10k raindrops and tracks them down the valley. The result is then augmented to achieve the final height-map. Other than with hydraulic erosion, no sediment map or velocity map are used here, so the computation much faster.
The code for the entire terrain computation (DLA, Perlin noise, Erosion and obj file export) is surprisingly short. Just about 400 lines of code.
Update: using stacked blur, the complete terrain with DLA, perlin & erosion can be computed in 4 seconds (1024x1024) on the CPU (single threaded).