We started by grasping the basics: a square is a 2D shape, while a cube is its 3D counterpart. But things got really interesting when we introduced the concept of fractals. Fractals are incredible shapes that have perfect self-similarity at every scale imaginable. This means that no matter how much you zoom in on a fractal, you'll see the same patterns repeating over and over.
The Menger Sponge is a fantastic example of a fractal. Imagine a cube with a unique twist: each face of the cube has a "window" pattern, where the middle cube is missing. This pattern repeats itself on every level of the sponge, creating a mesmerizing structure that seems to go on forever.
Our challenge was to create a Menger Sponge using business cards. Each cube is made from just six business cards, and a Level 1 Menger Sponge requires 20 such cubes. Our ultimate goal was to construct a Level 6 Menger Sponge, which meant using over 2400 business cards!
At first, building the cubes was tough. As Dylan shared, "The first 2 times we all tried to build the cubes, it was impossible. We tried; it was too hard, and we wanted to quit. We actually kind of quit and made Whaea Angel finish building them." Seb added, "They just kept breaking and falling apart; it was like magic."
But as Tegan wisely pointed out, "Did you know if we don't make mistakes, we would never learn anything new?" We took a step back to explore resilience, learning that things get easier every time you try, especially when learning something new. The next term, with the same demonstration and video, our class was ready. Within 10 minutes, without any help, the first boxes stood proud. Success and pride shone through the classroom.
Over the next few weeks, everyone mastered the art of creating cubes and joining them together. The class was abuzz with excitement as they constructed the first Level 1 cube. The challenge was on to see the Level 6 Menger Sponge take shape. This time, Whaea Angel wasn't needed at all.
A fractal is the same shape/pattern that zoomed in or out is exactly the same. The Menger Sponge's pattern is 3 x 3 cubes across the top and bottom of all sides with one cube on each side to join them. Basically, a window with the middle cube missing on each side. This pattern was repeated on each cube, getting smaller and smaller
Did you know a broccoli is a natural fractal, every part of the broccoli is the same as the larger part before it
Our journey into the world of fractals taught us much more than just mathematical concepts. It was a lesson in perseverance, teamwork, and the joy of discovery. Watching our skills grow and our confidence soar was truly rewarding.
