Celebrating Fibonacci Day with Visual Scripting

Every year on Fibonacci Day (11/23), designers, engineers, and mathematicians celebrate the elegance of a simple sequence that starts with the numbers 0 and 1. Take the sum of these two numbers and proceed to add the previous number to each successive result to produce the sequence. This results in the following series: 0, 1, 1, 2, 3, 5, 8, 13, etc. As we progress further along in this sequence, the ratio of two successive numbers approaches a special value, approximately 1.618, which is known as the golden ratio. This ratio appears repeatedly in nature - from pinecones to sunflowers to the spiraled chambers of a nautilus shell.

Biomimetic Architecture

As Fibonacci Day approached this year and I mulled over what to challenge myself to model, I arrived at an interdisciplinary objective: to create a conceptual architectural model inspired by something found in nature - the nautilus seashell. This cross-section of structural design and nature is known as biomimetic architecture, whose formal definition is the practice of designing buildings and structures by imitating processes and forms from nature.

Why Visual Scripting?

Visual scripting is often very helpful for specific use cases, including interdisciplinary endeavors, and this is no exception. Visual scripting uses a node-based modelling approach to create unique, robust geometry. It is especially powerful when dealing with varying patterns and complex geometry. There are two primary versions of this tool: one that runs in a web browser, called xGenerative Design, and the extensible desktop application called Visual Scripting. Working with fully parametric designs, organic shapes, and irregular patterns can be a major ask from more traditional CAD tools, so this is a good fit.

Building the Model

As I constructed the primary features of this structure, I kept the Fibonacci sequence in mind. Note how the first numbers of the sequence are incorporated. First, there is 1 spiral used for the outside profile of the structure. This creates the basic skeleton of the structure, but to fill it out and add some more depth, 1 more inner spiral is created, which overlaps the first and creates two separate spaces. The larger space complements the inner one in a straightforward display of self-similarity, a phenomenon known as fractals in nature.

The exterior surface of this structure is broken up into sections. This is done by getting a point sampling on the outside surface and using the Voronoi operator to create distinct sections. See this video for a discussion on this partitioning scheme: Voronoi Operator.

The color gradient operator is used in conjunction with a collection of mathematical operators to calculate and normalize the distances of the centers of the Voronoi sections. The further away the sections are from the center of the spiral, the deeper of a hue is applied to that section. I used 2 different shades of gold as a reference to the golden ratio: sunglow and harvest gold.

A new capability that was introduced in CATIA Visual Scripting 2026 is the Apply Material operator. This takes existing core or cover materials in the 3DEXPERIENCE platform and allows you to apply those materials to geometry in Visual Scripting. With this new capability, I applied 3 different materials to different features of the structure. Concrete is applied to the spiraled walls, ceramic to the roof, and a glassy, sand material for the floor.

The inside of the structure is separated into 5 chambers with a similar profile to the chambers of the nautilus seashell. Moreover, the radius of curvature for each of these barriers is derived by multiplying the distance between the endpoints by the golden ratio. Similarly, the width of the opening in this barrier is proportional to the curve length by the golden ratio as well. This keeps the proportions the same as the opening gets narrower, deeper into the structure.

Finally, the roof of the structure is designed to mimic the ridges of a seashell. Using one of the most common commands, Divide Curve, I divided the first revolution of the outermost spiral into 8 sections for this structure. After orienting the curves to the desired orientation, the operator that made the sweeping profile so easy is the Extrude to Point tool, which takes a given curve and tapers it down to a specified point in that direction. In this case, all the curves along the outside were extruded toward the center with this one command.

Conclusion

Inspiration is all around us, and patterns exist at every turn. As designers, we have the privileged opportunity to use our creativity to combine our observations of the world around us with cutting-edge technology, like Visual Scripting, to produce dazzling new outcomes.

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