Self-similarity is when all parts of an object are the same shape. Man made fractals are usually strictly self-similar meaning that each piece is exactly the same as the other pieces. In nature the pieces are simply self-similar meaning that there are small discrepencies between pieces. A fern leaf is self-similar. The smaller branching leaves look like the entire fern leaf. One of my favorite natural fractals that is an excellent example of self-similarity is the romanesque or broccoflower.