ok, here is the 1d version:
http://en.wikipedia.org/wiki/Midpoint_displacement_algorithm

hmm, never thought about that, you want to create sort of bubbles inside ?

hmmm, i will go on a train trip now, and when watching out of the window i will think about it
greets
 

i know that terrain generation lacks the feature of caves in the terrain, because it is just like the name sais, a heightmap,
hehe, i have not thought about ths yet, will come back later

cheers
 

<a href="http://www.prollcoder.com/flash/midpointdisplacementtest.swf" target="_blank">http://www.prollcoder.com/flash/midpointdisplacementtest.swf</a>

ok, i made a test for the 1d version, this generates a heightmap line, and additionally to the vertical displacement i simply add a horizontal displacement ...
and i came to the following method ....

first, the 1d version simply extends to 2d version, but i will talk only about the 1d version here

the midpoint displacement algorithm is good for generating heightmaps, it is not good for creating caves in those heightmaps, simply because a heightmap does
not feature this

my idea would be to set the displacement direction to the normal at that point
and i have just implemented this idea in another flash example, now true caves are generated, but some problems occur because of intersection of line segments ...
<a href="http://www.prollcoder.com/flash/midpointdisplacement_normal.swf" target="_blank">http://www.prollcoder.com/flash/midpointdisplacement_normal.swf</a>

the above algorithm could be extended to a 2d plane, producing a 3d object .... but it would be hard for game programmers to maintain a the players position within that thing ...

currently the algorithm works like this:

1.take a line segment
2.determine the mid point
3.determine the normal
4.determine the distance between the points
5.move the point in the normal direction by a random factor ( 0..1 ) multiplied by the halve distance between the original points
6. repeat with the new line segments until max iteration is reached

and when i am thinking about step 5, it could be improved that it does not use the halve distance between the original points, but that it uses the halve x distance of the points ...
wait, i will go and try this out, to avoid overlapping ...

just a moment ... oh, no, using only the halve x distance leads to quadratic results

ok, thats it for now with me ...

thx  i am working right now on a little overlap avoiding method

yes, this one is fine perlin noise/turbulence, you could use that as 3d value field and make an iso surface countour this is also a good way for generating 3d objects

Sockratease wrote >Found some Amazing Things in there, too!

:-)))
Margit