Thanks for playing, we're glad you like the visuals!
As for the growing spline, we have a source point and a target bezier curve in the simplest form. We build a binary tree with one root and a given number of leaf nodes, then place the root at a specified position and the leaf nodes uniformly along the target curve. The positions of the intermediary tree points (not leaves or root) are then iteratively modified via a procedure that tries to place each node between its parent and children, which results in the beautiful structure seen in the game.
We also add some additional effects - growing is done in the unity shader graph where each line gets thicker as time progresses, taking into account the tree structure; The whole tree except the root is moving a bit to simulate wind (which is sadly also the biggest problem since platforms are sometimes hard to get on because of the random movement); And we add particles on top of the leaf nodes. We are also able to compute the edge collider of the resulting tree (taking the wave effect into account), and combining that with the unity one-way platform effector enables the player to use the trees as platforms :D
If you are interested in more details, be sure to ask!