  The brain is probably the most complex organ in the human body. To understand
processes such as learning or healing after brain lesions, we need suitable
tools for brain simulations. The Model of Structural Plasticity offers a
solution to that problem. It provides a way to model the brain bottom-up by
specifying the behavior of the neurons and using structural plasticity to form
the synapses. However, its original formulation involves a pairwise evaluation
of attraction kernels, which drastically limits scalability. While this
complexity has recently been decreased to $O(n\cdot \log^2 n)$ after
reformulating the task as a variant of an n-body problem and solving it using
an adapted version of the Barnes-Hut approximation, we propose an even faster
approximation based on the fast multipole method (FMM). The fast multipole
method was initially introduced to solve pairwise interactions in linear time.
Our adaptation achieves this time complexity, and it is also faster in practice
than the previous approximation.
