  We report near-deterministic generation of two-dimensional (2D) matter-wave
Townes solitons, and a precision test on scale invariance in attractive 2D
Boses gases. We induce a shape-controlled modulational instability in an
elongated 2D matter-wave to create an array of isolated solitary waves of
various sizes and peak densities. We confirm scale invariance by observing the
collapse of solitary-wave density profiles onto a single curve in a
dimensionless coordinate rescaled according to their peak densities, and
observe that the scale-invariant profiles measured at different coupling
constants $g$ can further collapse onto the universal profile of Townes
solitons. The reported scaling behavior is tested with a nearly 60-fold
difference in soliton interaction energies, and allows us to discuss the impact
of a non-negligible magnetic dipole-dipole interaction (MDDI) on 2D scale
invariance. We confirm that the effect of MDDI in our alkali cesium quasi-2D
samples effectively conforms to the same scaling law governed by a contact
interaction to well within our experiment uncertainty.
