A random neuron fired in my brain and I was curious as to which grew
faster, Fibonacci or n^{2}. While I was at it I also plotted 2^{n}.

Well as it turns out Fibonacci grows faster than n^{2} but that's nothing
compared to how fast true exponential growth of 2^{n} grows.

Here's some pretty pictures.

Notice that the y-axis is logarithmic, exponential growth is *fast*!

If you have trouble imagining what that really looks like, here is with a linear axis.