Terrain Generation with Midpoint Displacement

I remember learning about midpoint displacement as a teen and having its recursive implementation blow my mind. At the time, I don't think I could ever implement it correctly because, like Steve notes here, most explanations really elide about bunch of details around how you do it. In particular, they aren't clear how you do two "stages" of midpoints: corners to sides, then sides to center.

Much later, I got it working, but I was disappointed with the visible seams it tends to lead to. After some trial and error, I came up with an algorithm I liked better for the game I was trying to write at the time.

I thought it was cool enough that I wrote a little tutorial. It's the very first piece of writing I ever put on the web, I think. It's still online (though, alas, I lost my old robot-frog.com domain ages ago):

http://stuffwithstuff.com/robot-frog/3d/hills/index.html

  (defn safe-average [a b c d]
    (let [total 0 count 0]
      (when a (add! total a) (inc! count))
      (when b (add! total b) (inc! count))
      (when c (add! total c) (inc! count))
      (when d (add! total d) (inc! count))
      (/ total count)))

Doesn't appear so safe against division by zero!

So is this a variant of this

https://en.wikipedia.org/wiki/Diamond-square_algorithm

Or is this exactly this algorithm?

> The diamond step. For each square in the array, set the midpoint of that square to be the average of the four corner points plus a random value.

> The square step. For each diamond in the array, set the midpoint of that diamond to be the average of the four corner points plus a random value.

Seems pretty straightforward. If you couple this with a deterministic random function, you could generate a terrain which always is the same, so that would make multiplayer possible.

That's obviously what you would want in game which is very large, without having a game which is too large to download.

Live demos were definitely helpful. Nicely done tutorial!

    $ man triangle
    NAME
     triangle - random mountains using iterative subdivision of triangles.

[…]

    $ /usr/lib/xscreensaver/triangle

If this stuff interests you there is a nice book called the fractal geometry of nature that has some interesting techniques.

http://www.amazon.com/Science-Fractal-Images-Heinz-Otto-Peit...

Thanks for sharing, this is very nicely documented.

Funny fact: it can be used as Grass Generator

Exponent: 7 Starting Spread: 35.3 Spread Reduction Constant: 20.5

This reminds me, does wisp work on Windows yet?