  We show that Directed Percolation (DP) simulations in a pipe geometry in 3+1
dimensions fully capture the observed complex phenomenology of the transition
to turbulence. At low Reynolds numbers (Re), turbulent puffs form and
spontaneously relaminarize. At high Re, turbulent slugs expand uniformly into
the laminar regions. In a spatiotemporally intermittent state between these two
regimes of Re, puffs split and turbulent regions exhibit laminar patches. DP
also captures the main quantitative features of the transition, with a
superexponentially diverging characteristic lifetime below the transition.
Above the percolation threshold, active (turbulent) clusters expand into the
inactive (laminar) phase with a well-defined velocity whose scaling with
control parameter (Reynolds number or percolation probability) is consistent
with experimental results. Our results provide strong evidence in favor of a
conjecture of Pomeau.
