Yan-Yang Ji; Zi-Yi Dai; Po-Cheng Wu
We are undergraduate students from three different departments at National Taiwan University. We took the course "Molecular Aesthetics" taught by Professor Bih-Yaw Jin during Spring 2020 semester. We constructed many interesting molecular models with beads and learned related scientific knowledges in class. As the course requirement, we need to design and construct a bead sculpture that contains scientific or mathematical meanings. After some literature search, we decide to construct a bead model for the fractal Menger sponge.
The Menger sponge is a cube-like fractal, which is a three-dimensional analog of the Sierpiński carpet. Earlier in the course, each student was given an assignment to construct a simple twelve bead cuboctahedral structure. From this, we realized that it is possible to implement a beaded representation of the Menger sponge based on these fundamental units. For this project, we constructed a total of sixty Level 1 sponges. The edge length of a Level 1 sponge consists of five fundamental units. The final Level 2 Menger sponge was then constructed by connecting these Level 1 sponges together.