We use numerical simulations of the time evolution of global textures to investigate the relationship between ordering dynamics and energy density in an expanding universe. Events in which individual textures become fully wound are rare. The energy density is dominated by the more numerous partially wound configurations, with median topological charge alpha ~ 0.44. This verifies the recent supposition (Borrill et al. 1994) that such partially wound configurations should dominate the cosmic microwave background.

10 pages uu-encoded compressed postscript including 2 figures. Accepted for publication in Physical Review Letters