# Reciprocal Fern Fronds

The fern is one of the basic examples of fractals. Fractals are infinitely complex patterns that are self-similar across different scales, created by repeating a simple process over and over in a loop. The Barnsley fern (Example here) shows how graphically beautiful structures can be built from repetitive uses of mathematical formulas.

## Fern Parameters

Due to the fractal nature of the fern fronds, the perimeter of the laser cutting took a long time. By simplifying this, I began joining fronds to each other and the large perimeter allowed for enough friction for the fronds to adhere to the adjacent one. I explored this through a series of 4 different frond types (X Axes on matrix below), angles of rotation (Y2, Y3) and distance between each leaf (Y4).

## Reciprocal Testing

With the study of many different arrangements of fronds and distances between each leaf in the frond, I was then able to select those that slotted in to the adjacent ones best and began arranging them with more components.

## Reciprocal Testing – Flat Component

The arching nature of each individual leaf meant the configuration was only stable once the fitting in of each component had passed the node of the arch. By flattening each component into rectangular members, the friction that allows the components to adhere to each other would be constant throughout the length of the individual part. This means they could now be placed more or less fitted in to the other component, as desired.

## Reciprocal Testing – Large Component

I then scaled up the component and attempted to array these as done with the smaller components above. Each component measured 600 mm length-wise and consisted of 5 members (3 facing one way and 2 facing the other, with a gap between them matching the width of each member). They originated from a central “stem” and attached to this by using glue and nails as to allow for easy manufacturing.

## Ferntastic Azolla

Simultaneously, I also became intrigued by a small aquatic fern called Azolla which I thought would be worth exploring too.

What is interesting about this little plant is that it holds the world record in biomass producer – doubling in size from 3-10 days. It is all thanks to its symbiotic relationship with the nitrogen fixing cyanobacterium, Anabaena. This superorganism provides a micro-climate in exchange for nitrate fertilizer.They remain together during the fern’s reproductive cycle. They also have a complimentary photosynthesis, using light from most of the visible spectrum.