If you are interested in a far more terrain like generation, the link casually mentions Diamond-Square at the bottom, but I wrote a post a while back that goes into much deeper detail, after looking at one of Notch's ludum dare entries.
Are there any systems out there that simulate the processes that go into forming real landscapes - geology, volcanoes, glaciation, water flow? [Just to list the main factors determining what I see in the local landscape here in Edinburgh every day - other places will have other factors].
Yes, there are systems but they aren't anywhere near geared towards real-time because they are basically very large Finite Element Analysis (FEA) problems.
You might be interested in Dwarf Fortress. Although it's not exactly what you just asked for, anyone who would phrase a question like that should fire up dwarf fortress at least once.
This reminded me all the hours I sunk into playing around with terragen (http://planetside.co.uk/). Definitely remember playing around in photoshop with filters (clouds! and difference clouds!... which I guess is just perlin noise) making height maps.
If you are interested in generating terrains with caves (or other formations with more that just a height detail) then I recommend following this chap http://procworld.blogspot.co.uk/
The technique is based on dual contouring a voxel field and his results are awesome. For info on how he went about it check posts from 2010 (most of it focuses on parallelization using cuda however)
This makes me think of how AoE II generated its maps randomly each time you play. They really had it right. It definitely multiplied the longevity of that game.
the white dot in the center is a control point that the user can drag around. That point defines a mountain. Height decays exponentially with distance from the control point. The height function is perturbed by an underlying noise function.
Edit: It's all done in JS/WebGL using a fragment shader and blatting the output onto static canvas elements. These are then composited for the larger image. It supports scrolling and zooming. I could never get the performance quite to where I wanted it.
And for another example: I wrote a terrain generator for the Abyss in Dungeon Crawl. Since the player is trapped in a hellish Lovecraftian place, the requirements for coherence are much more lax than Minecraft for example.
The algorithm defines some regular (columns, etc) and irregular (random walls) building blocks and then switches between them with Worley noise.
Minecraft also has biomes, which customise the terrain generation to produce regions of a particular type of terrain like forest, desert, sea, etc and some intermediary biome types like beaches. I don't know how it distributes the main biomes, but it may use one noise algorithm for that and another within each biome. Plus applying some rules to handle the borders between biomes. There is a lot more to it that just "It's Perlin noise".
One of my friends from school wrote a paper on a procedural terrain generation method that allowed simple user inputs to control the generation process.
Perlin noise is a kind of gradient noise. The difference is that, in a value-noise generator, you assign a random value (from some distribution) to each grid point, and then interpolate between the values. In a gradient-noise generator, you assign random gradients to each grid point, and then use dot products to produce the actual values from the gradients.
Value noise and Perlin noise are bother coherent noise functions based on integer lattices. Perlin noise is a type of gradient noise.
Value noise defines a pseudrandom value for each lattice point. Intermediate points are determined by interpolating the values of the adjacent lattice points. Value noise has discontinuous derivatives and looks blocky.
Gradient noise defines a pseudo-randomly oriented vector at each lattice point. To find the value of an intermediate point you interpolate the vectors.
If this stuff is interesting, I strongly recommend Texturing & Modeling: A Procedural Approach.
Yea, the blog shows us what Value Noise would produce, and says this is easily confused with Perlin Noise, but does not show us what Perlin Noise output looks like.
In Perlin noise, you set each grid point to a unit gradient vector, and then interpolate between them with a specific equation. This gives it useful mathematical properties, like being continuously differentiable, so the surface normals are smooth when you render it. That's not guaranteed with value
noise.
http://www.bluh.org/code-the-diamond-square-algorithm/