Fibonacci sequences appear in many places in nature . Some examples of the Fibonacci sequence being used in nature are tree branches , the pattern of leaves on a stem , the fruitlets of a pineapple , the flowering of artichoke , the uncurling of a fern and the arrangement of a pine cone . Fibonacci sequences appear in biological settings , in two consecutive Fibonacci numbers , such as branching in trees , arrangement of leaves on a stem , the fruitlets of a pineapple , the flowering of artichoke , an uncurling fern and the arrangement of a pine cone .