# Branching Structures

The inspiration for this body of work is the complex formations of tree branching. It is fascinating to comprehend the geometry of the branches and the reasoning for this, from aerodynamics to solar gain. The branching can be seen as fractal, with each branch migrating into two or more as it moves through space, also the thickness of the trunks is mathematically interesting, with Leonardo Da Vinciâ€™s deduction of the sum of branch thickness moving up the tree, at a certain height is equal to the thickness of the initial tree trunk. This analysis has been taken forward throughout these studies, creating more structurally sound physical and digital models. Through studying these geometries the work aims to produce architecture which is thoughtfully designed, and can be adapted based on its environment.

## Point Cloud Branching

Travelling through the point cloud the branching lines are created, although to produce a smoother geometry the initial branch lines are reformed with smooth curvature. Then, a pipe structure is applied to the branch lines, with varying thickness moving from top to bottom, as seen in the drawing above.

To form the point cloud branching system, first the path the branches aim to take must be formed, in the below case a cone shape was chosen to closely mimic the geometry naturally formed by the dragon-blood tree. Next a bounding box is created to inform the population of points. Once the points are established within the bounding box they can be joined to its nearest counter points, thus forming a point cloud.

## Pyramid Branching

1

The voronoi geometry is offset, with the distance halved each iteration.

2

The outer most geometry is divided into points which meet on the offset geometry.

3

The process of meeting the points continues.

4

Finally the points are all joined at a central point.

To form the 3D printed models the below file was used, is it comprised of 10 pyramid like branching structures, perfectly joined. Therefore the 3D printed model to the right could form the below geometry, if all of its counterparts were also printed.

## Curved Plywood Branching

Test 01

The initial test model using 0.8mm plywood utilises an initial layer of 8 segments. Once built the model had little tension, therefore needed string to create the dome like form. Although, even with the tension string the resulting form was flatter than anticipated.

Test 02

Proceeding the first test, the second aimed to produce a more substantial dome geometry. To do this 5 rather than 8 initial segments where used.
When the tension string was weaved the dome form was created, giving the model an ability to stand upright, as shown in the image above.

Test 03

The final test, aimed to decreased the percentage of material necessary to construct the model. This lead to cutting parts to make them thinner, causing breakage. Through the breakage, it was found that the dome like form could be created without the use of tension string.

## Curved Paper Void Branching

1
Initially points are set using populate tool in grasshopper, then the points are plugged into the voronoi tool, giving the geometry of meeting circular entities.

2
From the voronoi geometry, the curves are filleted, then offset, at an increment doubling each time.

3
On the outer curve points are set equidistant apart, from these points a mid point is set along the inner curve, then creating a line to the closest point on the inner curve.

4
The task of joining the points at their midpoint, along the closest point on the adjacent curve, is repeated. Finally the points all join together in the centre of the final curve.

5
Once all the branches meet at the central point of the final curve the offset curves can be removed to reveal the branching geometry.

Finally, tracing over the straight branching geometry with the curve tool. Revealing petal like closed curves filling the voids between the straight branches.