Right, after grueling combat with the beast that is mathematics. I have developed a fully working canyon generator, made solely out of functions.
What it can do:
Create a straight canyon of customizable width, depth and location.
What it can't do:
Make curved, or distorted canyon shapes, rotated canyon shapes (can be edited to go along the Z axis though).
However, this is an ongoing project (my way of following the excellent terrain from functions tutorials), and so the latter will probably be added later.
Below is a rendered result and the clip file, I added a power fractal to break up the canyon floor, a redirect shader to add detail to the walls, and some fake stones.
To use it, simply plug your terrain into the input, and plug the output into the compute terrain, move your camera to 0,x,0 (where x is a height of your choosing) and look down.
It is preset to work with the standard power fractal noise, but it will require modification to fit in if you change the feature scales. To modify it, check it's internal network, inside you will find all of the work that went into it. I'll post an editing guide if anybody's interested (and they can't find out from the intuitively-named nodes).
NOTE: As you can see from the background of my rendered image, this canyon BRAKES FOR NOBODY. There is no setup to restrict it to the low-lands, although I will tinker and see if I can add that in the future.
It would be great to have proper support for creating shaders out of clip files (with the ability to create custom dialogue boxes for them) but as it stands, this system is ok.
This generator can also be used to make troughs, rivers and dips, and with a quick modification the formulae can make cliffs as well.
Have fun playing with it!
