|
Menger sponge Lastly, we apply the Cantor gasket function to a cube in three dimensions, as shown in figure 5. This is known as the Menger sponge function, named after its architect Karl Menger. Similar to a Rubik's cube, it divides up the input cube into 27 (= 3 x 9) identical but smaller cubes. But, here, we throw away the center cube in each of six sides, plus the one in the core. So, in all seven small cubes are being removed, and hence leaving 20 small cubes in the Menger sponge of first generation. We again apply the Menger sponge function to each of the 20 small cubes. What we find is somewhat similar a Swiss cheese, but with square holes running perpendicular to each other. Here, Prog#5d is helpful to visualize the development of iterates of the Menger sponge function. (Project b - Classroom construction of Menger sponges)
Figure 5. Menger sponge
|
