  Can uncorrelated surrounding sound sources be used to generate extended
diffuse sound fields? By definition, targets are a constant sound pressure
level, a vanishing average sound intensity, uncorrelated sound waves arriving
isotropically from all directions. Does this require specific sources and
geometries for surrounding 2D and 3D source layouts?
  As methods, we employ numeric simulations and undertake a series of
calculations with uncorrelated circular/spherical source layouts, or such with
infinite excess dimensions, and we point out relations to potential theory.
Using a radial decay 1/r^b modified by the exponent b, the representation of
the resulting fields with hypergeometric functions, Gegenbauer polynomials, and
circular as well as spherical harmonics yields fruitful insights.
  In circular layouts, waves decaying by the exponent b=1/2 synthesize ideally
extended, diffuse sound fields; spherical layouts do so with b=1. None of the
layouts synthesizes a perfectly constant expected sound pressure level but its
flatness is acceptable.
  Spherical t-designs describe optimal source layouts with well-described area
of high diffuseness, and non-spherical, convex layouts can be improved by
restoring isotropy or by mode matching for a maximally diffuse synthesis.
  Theory and simulation offer a basis for loudspeaker-based synthesis of
diffuse sound fields and contribute physical reasons to recent psychoacoustic
findings in spatial audio.
