Experiments on xenon dendrites growing in a three-dimensional volume o
f pure, supercooled melt have been performed. The shapes of the dendri
tes have been determined with high lateral resolution. The dendrites g
row in a stable mode and do not show oscillations in the growth veloci
ty nor in the curvature of the dendrite tip. The dendrites do not have
the shape of a paraboloid of revolution. Surface anisotropies determi
ne the shape of the dendrites. Four fins grow along a dendrite. The co
ntour of these fins can be described by a power law z similar to \x\(b
eta) with beta approximate to 1.67. These experimental results are in
agreement with the analytical work of E. Brener [Phys. Rev. Lett. 71 (
1993) 3653]. Both experiments and analytical work are compatible with
the assumption that thermal fluctuations initiate side branching. Tip
oscillations can be excluded.