So here's the equation we're working with
Number of small copies = magnification factor to D power
And D is the self-similaty dimension That's what we're interested in
So first, for this shape how many small triangles do I see in the big triangle?
Well 1, 2, 3, 4 so the number of small copies is 4
What about the magnification factor?
How much do I have to magnify or strech this triangle by or any of the other ones, so it's as big as this one
And the answer is 2 And to see that maybe look at this length
between my two fingers here So to go from this triangle to this triangle
I see I have to take this length and make it twice as large Or you can see that this length
of the full triangle has two, 1, 2 triangles there
So that means the magnification factor is 2 So this is the equation
and then we want to figure out the dimension D and we can see
that D is 2. Why? Because 2 to the 2
if I plug in D equals 2 gives me 4
So that means the dimension of this object is 2
It's two dimensional And that makes sense
We know that triangles are two dimensional They live in a plane
They, uh, extend in two different directions
So we haven't learned anyting new about triangles we've known that they're two dimensional
But this is another example to show how this formula works
So, next we'll use this formula on a fractal and we'll see what we get