# Fibonacci Trees

Several of the Sareoso diagrams feature Fibonacci trees. One of these is the Zuhamua Aldi diagram shown below: The diagram shows a tree or vine shape (the name of the diagram means “tree/vine of Aldi”, and the label ILAR means “pea”), so perhaps this is a pea plant. Snow Pea Flowers (by Bmdavll via Wikipedia)

The shape shows the possibilities of branching by dividing into two at each stage, so that the shape could grow by doubling: 1, 2, 4, 8, 16, 32, 64. But these possibilities are not all realised – in this diagram, the unrealised possibilities are represented by little spiral tendrils (by which a vine takes hold of its supports).

This results in slower growth, according to the Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21. Growth according to the Fibonacci sequence is very common in nature, for example in spirals, branching and flower patterns. There is a good overview of the Fibonacci sequence and the way it appears in nature at Ron Knott’s Fibonacci Numbers and Nature page.

The way the structure is represented in the diagram isn’t random: it follows a simple rule. Each branching-point is represented by one of six two-letter codes or “doubles”. For example, at the base of the tree is found the double AT.

A double has the possibility of branching into two others, which have to start with the same letter as the first one finished with. For example, AT can be followed by TA or TE. Branchings which revert to the previous double are not allowed though. For example, there is no problem with AT-TA-TE, but AT-TA-AT is not allowed because it goes back to AT.

Out of all the branches, there are only three that ‘bear fruit’ in the diagram. These are branches which go through all the six doubles exactly once, without repetition.

The Sareoso diagram Erregaluak shows all three of the ‘vines’ from the Zuhamua diagrams together, radiating out from the centre. Instead of the double letters, shapes are used, with the outer shape equivalent to the first letter, and the inner shape equivalent to the second one. The diagram Zuhaitza Bizi gives a similar tree, but using three shapes instead of two (adding a middle shape). This shows similarity to the tree in Chapter 6 of the Book of Jubilee.