  A graph $F$ is called a fractalizer if for all $n$ the only graphs which
maximize the number of induced copies of $F$ on $n$ vertices are the balanced
iterated blow ups of $F$. While the net graph is not a fractalizer, we show
that the net is nearly a fractalizer. Let $N(n)$ be the maximum number of
induced copies of the net graph among all graphs on $n$ vertices. For
sufficiently large $n$ we show that, $N(n) = x_1\cdot x_2 \cdot x_3 \cdot x_4
\cdot x_5 \cdot x_6 + N(x_1) + N(x_2) + N(x_3) + N(x_4) + N(x_5) + N(x_6)$
where $\sigma x_i = n$ and all $x_i$ are as equal as possible. Furthermore, we
show that the unique graph which maximizes $N(6^k)$ is the balanced iterated
blow up of the net for $k$ sufficiently large. We expand on the standard flag
algebra and stability techniques through more careful counting and numerical
optimization techniques.
