  We consider a discrete-time binary branching random walk with independent
standard normal increments subject to a penalty $\b$ for every pair of
particles that get within distance $\e$ of each other at any time. We give a
precise description of the most likely configurations of the particles under
this law for $N$ large and $\b,\e$ fixed. Particles spread out over a distance
$2^{2N/3}$, essentially in finite time, and subsequently arrange themselves so
that at time $2N/3$ they cover a grid of width $\e$ with one particle per site.
After time $2N/3$, the bulk of the particles and their descendants do not move
anymore, while the particles in a boundary layer of width $2^{N/3}$ form a
``staircase" to the particles in the bulk. At time $N$, each site in the
boundary layer is occupied by $2^{N/3}$ particles.
