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.

Marimba Membrane

Coming from a family of artists and musicians I decided to focus my research on the relationship between music and wood how this could be represented in a larger, playful structure of sounds.

Pythagoras discovered that by hitting an object with a hammer weighing half as much as another (a fundamental note), it produced a vibration frequency or musical note twice as high 2:1 (Octave). By hitting it with a hammer weighing 3:2, it sounded a fifth apart (Perfect Fifth) and a hammer of 4:3 the weight, sounded a fourth apart (Perfect Fourth).

The vibratory curves occur within the struck object and emit varying sounds that we find to be consonant (attractive to hear) and we relate these to musical scales. All other musical notes apart from the fundamental, produce additional frequencies which can be heard simultaneously. They are known as overtones and produce what is known as timbre, allowing a musical note to be heard for more time.

The overtones can be specifically shaped through the tone bars of a Marimba, differentiating itself from the xylophone because of this. The curved, undercut part of a tone bar is responsible for the fundamental note and two additional overtone frequencies, giving this instrument a great timbre.

The fundamental tone produces its vibratory waves with an antinode (marked in green) in the centre of the tone bar. All three variations of the vibratory waves present a node (marked in red) on the extremes of the bar, an opportunity to create a whole to fix them without affecting the note.

The length, width and depth affect the fundamental tone’s frequency: increasing either one with decrease the musical frequency, producing a deeper musical note. Additionally, the orientation and type of wood used will affect the musical note due to its density and capability to transmit sound. I chose to use Poplar for this project due to it being a low-density hardwood (500 Kg/m3) with not many knots and a good capability to transmit sound (5080 m/sec).

In order to form a large structure, I decided to support the tone bars through a tensegrity membrane similar to the Moom Pavilion. The tone bars are aligned in rows, which are fixed on both ends and individually act in compression. Tension cables join each tone bar to the adjacent ones through the vibratory waves’ node. Each row of tone bars is half offset to the adjacent row. The combination of diagonal tension and linear compression gives the structural integrity and creates a vertical lift.

Through digital explorations, I was able to configure a tunnel-like structure that would support 39 tone bars in 7 rows: 4 rows are composed of 6 tone bars each and sitting intermittingly between them are 3 rows of 5 bars each. Through Grasshopper I was able to automate the process of finding the dimensions for each tone bar according to the desired musical note. Each tone bar was then individually cut and sanded down by hand for the desired overtones before being arranged into a grid and joined with cables, crimps and cable tensioners.

The two adjacent extremes of each row of tone bars were fixed to a base I created to anchor them. The most challenging part of this structure is to accomplish the correct tension for it to form a uniform arch. By expanding the base, additional rows of tone bars can be joined laterally to form a larger range of tone bars with an even larger scale of musical notes.