  We have observed the formation of gluon flux-tubes within baryons using
lattice QCD techniques. A high-statistics approach, based on translational and
rotational symmetries of the four-dimensional lattice, enables us to observe
correlations between vacuum action density and quark positions in a completely
gauge independent manner. This contrasts with earlier studies which used
gauge-dependent smoothing techniques. We used 200 O(a^2) improved quenched QCD
gauge-field configurations on a 16^3x32 lattice with a lattice spacing of 0.123
fm. In the presence of static quarks flux tubes representing the suppression of
gluon-field fluctuations are observed. We have analyzed 11 L-shapes and 8 T and
Y shapes of varying sizes in order to explore a variety of flux-tube
topologies, including the ground state. At large separations, Y-shape flux-tube
formation is observed. T-shaped paths are observed to relax towards a Y-shaped
topology, whereas L-shaped paths give rise to a large potential energy. We do
not find any evidence for the formation of a Delta-shaped flux-tube (empty
triangle) distribution. However, at small quark separations, we observe an
expulsion of gluon-field fluctuations in the shape of a filled triangle with
maximal expulsion at the centre of the triangle. Having identified the precise
geometry of the flux distribution, we are able to perform quantitative
comparison between the length of the flux-tube and the associated static quark
potential. For every source configuration considered we find a universal string
tension, and conclude that, for large quark separations, the ground state
potential is that which minimizes the length of the flux-tube. The flux tube
radius of the baryonic ground state potential is found to be 0.38 \pm 0.03 fm,
with vacuum fluctuations suppressed by 7.2 \pm 0.6 %.
