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Serpenski Triangle - A Nice Fractal

Playing with the fractal

What pattern do you notice with the fractal as you increase n?

The Perimeter

Play with increasing n, how does the perimeter change?

Perimeter 2.0

What value do you think the perimeter is growing to?

The Area

Play with increasing n, how does the area change?

Area 2.0

What value do you think the area is growing to?

Dimension

Do you know of any dimesion (1D, 2D, 3D, ...) where the shapes area and perimeter scale like so?