As a was lying on my back in the University park to day, resting a bit between reading papers (more on that later), I looked up at a pine tree and asked myself a very computer sciencey question. How does the number of needles *L* on the tree grow, as the tree grows taller? If the height of the tree is *h*, what is the size of L?

## Exponential?

I initially thought that surely this must be exponential, after all just think of a binary tree: The number of leaf nodes in a balanced binary tree of height *h* is . So maybe: