Plants and matrices

I am starting a "Tree simulator" and I'm trying to make it so I have a single component that generates the 3D shapes for the stem, branches, leaves, etc...

I quickly ran in the math problems, and basically I don't really know where to start on

Let's say I have Stem_A at [0, 0, 0] with a length of [0, 1, 0] and no rotation. When some condition is met, a second smaller Stem_B starts growing from Stem_A at a 45° angle on the X plane and a random rotation around the Y plane. So far so good.

The big question I have is "how do I grow Stem_C from Stem_B with the equivalent 45°X+rand()°Y transformation"?. Since Stem_B is no longer aligned with the axis, I lost the supe-easy referential... I understand that I should be able to represent that transformation with a 4x4 matrix, but I have no clue on how to set it up and how to use it in this context...