Good formulas for terrain?

I’d like to be able to generate terrain for some 3D work I’m doing, but I can’t seem to find any good formulas that are randomish-looking. Google is turning up an impressive sparsity of help. Most solutions depend on an iterative sequence, which I don’t want. Others are links to research papers that only shows the abstract, but that I probably wouldn’t understand even if I could read. I don’t want to use random numbers either, if possible.

Coolest would be if there’s like an encyclopedic listing somewhere of what various formulas look like, graphed. But if anyone knows of some good ones to look up, just say.

Most of the simple techniques I’ve seen are some kind of iterative process - fractal generation where you start with a triangle, subdivide it into 4 triangles, move the newly created vertices up or down, and repeat.

There was some interesting stuff in one of the early Game Programming Gems books, for Sim City where they simulated fault lines and erosion to get a more natural look than what the basic fractal algorithms give you.

If you don’t want to do any iteration over the whole terrain I’d think you need some kind of randomness / noise. You might want to check out Perlin Noise - its sort of smooth randomness, and you can do some cool stuff with it. You’d be able to generate one point (or triangle, whatever) at a time, and you can set up the perlin noise function so that you generate height values entirely from X and Y positions, with no other randomness involved.

I’d have to say though, all those still look a little artificial. One of the easiest things to do to get very natural looking terrain is to poke around on the US Geographical Survey web site. They have free elevation images (National Elevation Data - in TIFF and other formats) that you should be able to turn into 3d models. Try here, though the website’s been pretty unresponsive for me tonight: http://seamless.usgs.gov/website/seamless/viewer.htm

The virtual terrain project has a ton of info too, and links to source data - though is focused on visualizing real-world terrain, not generating new terrain. http://www.vterrain.org/

What software are you using?

There are a number of packages out there designed to create 3d landscapes.

Vue7 Pioneer is free to use.

There’s also Bryce from Daz3d.

I would also try visiting the forums at those two sites. There’s plenty of links to other sites, and tutorials covering a wide range of subjects. Renderosity for example has a number of tutorials for various programs.

Even if you’re using something these sites don’t cover, or need a different approach to what’s on offer. There’s probably some tips and tricks you can convert.

This is something I’ve just started looking into. And, speaking as someone with absolutely no artistic talent at all, I’m having a ball.