Understanding the twiddle factors So I've been looking at this butterfly diagram to try to understand it better:

And I am trying to get a good understanding of the twiddle factors.
The definition is given as:
FFT Twiddle Factor: ${e^{i2{\pi}k/N}}$
and
IFFT Twiddle Factor: ${e^{-i2{\pi}k/N}}$
So k is the index number of the iteration thus $k=0,1...N$ but its $N$ that I am unsure of.
From the image is the first stage N = 8 (since there are 8 butterflies) or is N = 2 since each butterfly only spans two elements? Or is N always 16 every pass?
My guess currently is:
Stage 0 : N = 8
Stage 1 : N = 4
Stage 2 : N = 2
Stage 3 : N = 1

Am i correct in this assumption? If not i hope some one clarifying my misunderstanding here.
Thanks
You got it mostly backwards, but otherwise OK :)
This can be pretty directly answered by writing down what the Cooley-Tukey FFT's twiddle factor $W_N$ is:
$$W_N=e^{-i\frac{2\pi}{N}}$$
and that's it. For example, in your picture, in Stage 0, you're multiplying with $W_2^0=\left(e^{-i\frac{2\pi}{N}}\right)^0=e^{-i\frac{2\pi0}{N}}=e^0=1$.

So k is the index number of the iteration

No, $k$ is the exponent of your twiddle factors. It goes from 0 to half the size of your transform (in each stage).

From the image is the first stage N = 8 (since there are 8 butterflies) or is N = 2

Stage 0 has subtransforms of size N=2, as you can see. (Also, just write down the 2-DFT's formula and compare.)