# Fractal Voronoi

# Abstract

**Fractal Voronoi** aims to produce a design with fractal behavior, which can later be imagined in the site i.e. **Barcelona Pavilion** by Mies van der Rohe. Fractal design refers to a curve or geometrical figure, each part of which has the same character as the whole. They are useful in modelling structures (such as snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth and galaxy formation.

## Concept

The design works on the concept of making a fractal design with the basic concept of Voronoi Design.

**Voronoi diagram**is a mathematical formula used in many scientific fields and use of that goes as far as Descartes. The

*source*

## Grasshopper Code Generation

### Pre-Loop Code

The process is to make a **rectangular surface** with the dimensions of the slab of the Barcelona Pavilion. Then to populate the surface using **Populate 2D**. Later the **Voronoi Code** is used to created a voronoi surface. This surface is later **deconstructed** into defined faces and edges from which center can be obtained. This center can be used to **scale** the defined surfaces down to make a new surface which can be moved on **z-unit** to create a **loft**. This loft is the input that the Anemone will use to create fractal loop. The grasshopper code below is the code used in the design.

### Anemone Loop Code

The Lofted Voronoi Geometry is created before the loop as this loft will have a different height than what we need in the fractal design. This is why there is another loft function inside the loop with smaller height so that a defined set of loop is being created without any surfaces intersecting one another. The loop consists of **loft commands, voronoi command and an exit point command **that are connected to different data points- D0, D1, D2. All the data are set under the loop and then fractal brep is created in the end which is later smoothened with the use of **Weaverbird’s Mesh Thicken** and **Weaverbird’s Catmull-Clark Subdivision. **You can also give the design color with the help of Custom Preview.

# Iterations

# Animation

# Renders

#### Credits

**Algorithmic Emergence // Fractal Voronoi **is a project of IaaC, Institute for Advanced Architecture of Catalonia developed at **Master in Advanced Architecture** in **2020/2021** by:

*Student: Shubham Dahedar*

*Faculty:*

**Rodrigo Aguirre**

Assistant**: Ashkan Foroughi Dehnavi**