This article sheds some light onto what the Fibonacci Rabbit Riddle is.

## The Fibonacci rabbit riddle illustrates a self accumulating growth sequence.

The origins of the riddle are quite interesting. It was actually a side note to a much bigger discovery Fibonacci had made which he was explaining in a book. This discovery is actually Fibonacci’s much bigger legacy which is completely overlooked.

### About the Fibonacci Rabbit Riddle chart…

A couple of important tips before your wreck your head on overthinking this, as I did…

- Forget all your common sense questions like ‘what if only males are born?’ or ‘surely some would die’. In this thought experiment all Rabbits live and all mature pairs reproduce another pair (one male and one female) within each step of the chart.
- Think of each pair as a single unit (this is the bit that got me confused for ages) we are counting PAIRS of rabbits as a unit,
*not*single rabbits.

Small rabbits are the newly born ones. These will take one full step of the chart to mature to an adult (larger) pair. All adult pairs will always breed another pair at every step (blue arrows). The red arrows show the continued existence of a rabbit pair from the previous step.

## What is the Fibonacci Rabbit Riddle?

The analogy of breeding rabbits is used to show a growth rate that is in relation to itself. A self accumulating sequence. The number of rabbits born at each step of the chart is a Fibonacci sequence number that holds a special relationship to the whole of the population.

The numbers on the right hand side of the rows are the TOTAL number of pairs at each step, the population of pairs. These are also the Fibonacci sequence numbers.

## In relation to the whole.

A growth rate that is in relation to the whole population.

The relationship is the ɸ Phi ratio.

The What are the Fibonacci numbers? article explains how to generate the Fibonacci sequence and the ɸ ratio between them. This article is just dealing with rabbits to illuminate the self accumulating growth process.

## What is self accumulating?

Notice how no new rabbits arrive from outside this family. It is a self accumulating growth process. The population total at each step arises from what is already in existence from the immediate step before.

Each rabbit on the bottom row can be traced back up the arrows to the point it was born (blue arrow) and its parents. Those parents can be traced back further still. So in each rabbit can be traced back to the original Rabbit.

Each term [of the Fibonacci sequence] may be traced back to its beginning as unity in the Monad, which itself arose from the incomprehensible mystery of zero

Micheal Schneider

The take away here is to remember this principle of **ongoing growth from within**. This pattern, once understood, can be see through all rhythms in nature on ALL scales.

## Activities using the Fibonacci numbers and Rabbit Riddle

I have many activities that discover this pattern of growth within natural forms (eg: painting the pinecone) but this article is to do with the Fibonacci Rabbit Riddle. So I have made the chart image into an A4 version for ease of printing and also included versions of the chart with just the rabbits and one with just the arrows. Also a page of just rabbit pairs if you want to do something else with them.

These charts can be used to explore the self accumulating growth process by:

- Add your own arrows to follow the growth rate
- Add your own rabbit pairs (or other forms) to experience the growth
- How many new rabbit pairs in each step (blue arrows)?
- Trace back each rabbit pair to identify parent or grandparent pairs.
- Which rabbit pair is the oldest?
- How many baby pairs has each pair had?
- Can you see a pattern in the amount and occurrence of the blue arrows (baby pairs)?

## Fibonacci branching patterns

If we take the image of just the arrows and turn it upside down, you might begin to notice a similarity in what you see here to another common form in nature. Its a very robotic sort of tree, but it resembles a tree none the less. Imagine the trunk has aged to be much thicker over the years and some branches generate shorter or longer new branches (nature is never perfect).

If you break off any branch from this tree, you will see it resembles the whole. It is a smaller version of the whole tree.

And here is where this article stops. We have examined the Fibonacci Rabbit Riddle and seen how it grows of itself. We have touched on the relationship to Phi.

From here begins our understanding of Fibonacci and Fractal symmetry, which I will come to later.