This is how I do randomly wandering roots, it should work for birch or pine, but standard oak doesn't work as easily*. This method really helps you feel like you are "growing" a root system, and avoids the problem I had the first time with a surface terraformed with logs or log patterns.
This shows two blocks of root going up from a top down perspective. I plant a torch at the end of the root, and 3 saplings on the other side of the root as the picture shows. Eventually one of them grows.
When I revisit, it looks like it does in the second picture, with a full grown tree above the disconnected log. I pick up the ungrown saplings, and torch, and place a log block where the torch was. I leave the bottom log, to incorporate it into my root system, and chop down the rest of the tree. Now we are back to square one, the end of a root.
I like to follow the random direction it chooses and place my torch in line with that direction, then arrange the saplings around it, the middle one in line, and one on each side. This makes roots that randomly wander over the landscape.
Random isn't always good, this shows a root that tries to circle around on itself. This is an example of this method delivering a result I am not happy with. Another example is if you wanted your root to go mostly in one direction, but wanted to incorporate some randomness. By altering the sapling and/or torch placement, can bias or limit its possibilities without just placing roots arbitrarily where you want them to go.
I tried out doing it like this, but felt it made turns too densely and quickly. Your milage may vary, but I found extending the root in 1 block the direction it chose made it look better.
*For Pine and Birch, when one tree grows it excludes the rest of the saplings. With birch I have seen 2 grow when one is short and the other is tall and they are 2 apart, I figure thats a good place to fork out into 2 roots. With oak, the other trees arent excluded, just limited to using the 10% (33% rain forest) big tree growth algorithm. If there isn't a solid trunk shortly above it, the oak sapling will eventually grow. If you check frequently this method can still work with oak, but if the saplings are given excessive time, you may find all have grown.