Burls not only occur only at the base of the tree, but can grow anywhere on the tree. In the picture below, the strange growth on the side of the tree is a burl. You may have seen redwood trees with two trunks. Redwoods are able to grow two trunks on the same tree when damage has occurred, and burl tissue starts growing. The burl on this tree trunk looks like an old man with a beard.
Burls come in all shapes and sizes.
Photo by Jim Baird. Often, burls will have root sprouts growing downward from their bases. The ability to sprout new roots helps these trees survive floods. Flood waters deposit silt around the bases of the trees, smothering most trees. Redwoods however, can grow new roots into the newly deposited soil, enabling the tree to survive.