| 1 Dimensional | 2 Dimensional | 3 Dimensional | Additional | |
|---|---|---|---|---|
| Cantor Sets | Ternary (1/3)
|
Ternary (1/3)
|
Ternary (1/3)
|
|
| Sierpinski Gaskets | Ternary
|
Ternary | ||
| Another Possibility | Ternary |
Cubical Sierpinski. Externally the cubical sierpinski looks like a solid cube. Internally it has as many holes as a sponge. Think of it as a sponge wrapped in solid foil.
Another Possibility. This construction produces a cube with one cave having 6*3^(2*n-2) holes at the nth iteration (n=1, 2, 3, ...).
Note that with an increase in dimension, the number of ways to cut out pieces increases. One for 1D, two for 2D, three for 3D.
What if these constructions were modified to work on different shapes? Find Out!
What if we looked at the complements of these constructions? Find Out!
If you haven't seen enough, check out the following fractal inspired objects.
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