Fractal Branching in the Victoria Amazonica

Much can be learned from the biological system of the Victoria Amazonica, also known as the Giant Water Lily. The plant has long generated curiosity about its delicate appearance yet impressive strength which is owed to its exceptional structural characteristics. An intricately webbed system of spines and ribs contributes to the success of the Victoria Amazonica, as it evenly distributes the weight of the plant while leaving pockets to store air and increase buoyancy. Once studied in detail, the branching pattern of the spines and ribs becomes apparent. Each Water Lily is unique, but all follow the same fractal branching pattern which can be defined by the following geometric sequence:

This branching system proves to be most effective for the Victoria Amazonica. Therefore, because of the efficiency of the system, its quick growth, and incredible strength, the plant can become somewhat of an invasive species. While the Lily Pad remains planar, in different forms, its system proves to be equally as strong. Below, the application of the system to different forms is tested.

Ribs are evenly dispersed between spines, lending to the plant’s equally distributed surface weight. In this example, the ribs are roughly spaced 8.3 cm from each other. This can be described with the linear expression: y=(1/8.3)x

Finite Element Method Mesh structurally analyzes how the surface of the Lily Pad is broken up into geometric cells. The FEM of the Pad can be tested for its movement under force and for its elasticity . These diagrams were generated with data from Nature-Inspired Fractal Geometry and Its Applications in Architectural Designs. Asayama, Riane, Sassone. 2014.

Naturally, the model without ribs (left model) was not as strong. However, it had more potential for movement and was still structurally impressive. Going forward, this was used as a base model for form studies.

As the above models proved to be structurally sound, they were scaled up to test their application to a larger model. At 1.5 m, the structure was not as stable because the spacing of the branches increased. Going forward, increased branching will be tested. Added weight will also be applied to see how it affects the stability.