  Self-propelled colloids constitute an important class of intrinsically
non-equilibrium matter. Typically, such a particle moves ballistically at short
times, but eventually changes its orientation, and displays random-walk
behavior in the long-time limit. Theory predicts that if the velocity of
non-interacting swimmers varies spatially in 1D, $v(x)$, then their density
$\rho(x)$ satisfies $\rho(x) = \rho(0)v(0)/v(x)$, where $x = 0$ is an arbitrary
reference point. Such a dependence of steady-state $\rho(x)$ on the particle
dynamics, which was the qualitative basis of recent work demonstrating how to
`paint' with bacteria, is forbidden in thermal equilibrium. We verify this
prediction quantitatively by constructing bacteria that swim with an
intensity-dependent speed when illuminated. A spatial light pattern therefore
creates a speed profile, along which we find that, indeed, $\rho(x)v(x) =
\mathrm{constant}$, provided that steady state is reached.
