Originally Posted by John Sehi
When I first thought of dimensions, I thought about the usual 1-D, 2-D, and 3-D. I did not examine it farther, did not think that there would be a need for any more thought. A fractal dimension was something I didn’t know about. I didn’t really question their existence, but more of something that’s not talked about. Since learning about the Middle Thirds Cantor Set in which is less than one dimension and the Sierpinski Triangle that is between 1-D and 2-D, this just fascinated me. Especially the Menger Sponge which has infinite area but no volume.
I am surprised at what can be done with fractals. There are so many possibilities with fractals that it is sometimes hard to comprehend all that can be accomplished with mathematics.