Pattern Selection

The Fibonacci sequence is present in natural patterns such as the arrangement of leaves, pine cones, and sunflower seeds, but also in art and mathematics. This sequence can be visually represented by a logarithmic spiral. Its relationship with the golden ratio makes it even more interesting.

Creating a 3D representation of the Fibonacci sequence will allow museum visitors, especially those with visual impairments, to understand the relationship between mathematics and nature through touch, experiencing the orderly arrangement of natural elements.

The Fibonacci sequence is a series of integers where each term is the sum of the two preceding ones. It starts with the numbers 0 and 1 and can be mathematically expressed as F(n) = F(n-1) + F(n-2), where F(n) represents the nth term of the sequence.

Fibonacci in Nature: The 3D Model

The shell of a snail is a natural form that follows a pattern that mimics a logarithmic spiral. As the Fibonacci sequence progresses, the quotient between two consecutive terms will approach the golden ratio (approximately 1.618). Although the snail's shell does not absolutely show the numbers of the Fibonacci sequence, its shape and geometry are closely related to the sequence and the golden ratio.

Materials and Manufacturing Technology

We will use Fused Deposition Modeling (FDM) 3D printing technology with an Original Prusa MK4 printer, combined with the use of polylactic acid plastic (PLA).

PLA is an ideal material choice for this project as it is biodegradable, hence sustainable and environmentally friendly. Additionally, it is easy to use in 3D printing as its relatively low melting temperature offers minimal shrinkage and does not emit harmful gases during printing.

FDM technology is one of the most common and affordable in the field of 3D printing as it allows the creation of complex models with a high degree of precision. This technology works by depositing successive layers of melted material (in the case of this project, it will be PLA), which cool and solidify to form the final object layer by layer.

Finally, the Original Prusa MK4 3D printer is the latest addition from the company as of now (13/05/2023), a machine of great precision, reliability, and with a huge user community, which can provide support and advice in any case.

3D Model Preparation

The fact that the snail shell model is hollow inside will help save material and printing time. Moreover, we will split the model into two parts with flat surfaces to achieve more stability and avoid using supports since both parts can be printed with the flat side on the printer base.

3D Model Slicing

Configure the print as follows in the upper right panel (G-CODE Provided):

• Layer height 0.15mm with quality profile.
• Prusament PLA filament.
• Original Prusa MK4 printer with a 0.4mm nozzle.
• 70% infill to make it rigid.

Model Assembly

With the two parts of the snail shell printed, they will need to be joined using the following procedure:

• Preparation of the joining surfaces using fine sandpaper to smooth the flat surfaces of both halves, thus ensuring that the union is more solid.
• Test that the fit fits correctly.
• Apply "super glue" (cyanoacrylate) to both contact surfaces.
• Carefully join the two parts, ensuring they are well aligned, while holding them together manually for a few minutes.
• Leave the piece to dry without handling it for a few hours.
• For the final finish, if necessary, more sandpaper can be used to smooth any excess adhesive or imperfections at the joint. Also, the option of painting or varnishing the piece to improve its appearance or protect it from touch can be considered.