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- Summary
- I got a bit confused on how they were supposed to be measured (maybe fractal dimensions too?)

I was trying to find some sort of pattern in the triangle (below) to graph it or find some equation, and I thought maybe measuring something would be a good idea.

I was okay just calculating the area for the first few iterations, but then I got confused on how I was supposed to represent like an infinite term? Because the ones that have a fixed number of little triangles all have (I think) area since they stop subdividing, so I could get those numbers.

But from what I think I read the actual fractal that goes on forever wouldn't have an area since it would just be never ending lines? Also, there's the Hausdorff/fractal dimension which is saying it's between 1D and 2D, so then is there no way to "measure" it (like as area/length/volume) when it is the actual infinite fractal?

If so, would the graph just be always approaching zero, or would it eventually become zero since it's only made up of lines?

Thanks!

I was okay just calculating the area for the first few iterations, but then I got confused on how I was supposed to represent like an infinite term? Because the ones that have a fixed number of little triangles all have (I think) area since they stop subdividing, so I could get those numbers.

But from what I think I read the actual fractal that goes on forever wouldn't have an area since it would just be never ending lines? Also, there's the Hausdorff/fractal dimension which is saying it's between 1D and 2D, so then is there no way to "measure" it (like as area/length/volume) when it is the actual infinite fractal?

If so, would the graph just be always approaching zero, or would it eventually become zero since it's only made up of lines?

Thanks!