  Spatial chaos as a phenomenon of ultimate complexity requires the efficient
numerical algorithms. For this purpose iterative low-dimensional maps have
demonstrated high efficiency. Natural generalization of Feigenbaum and Ikeda
maps may include convolution integrals with kernel in a form of Green function
of a relevant linear physical system. It is shown that such iterative
$nonlocal$ $nonlinear$ $maps$ are equivalent to ubiquitous class of nonlinear
partial differential equations of Ginzburg-Landau type. With a Green functions
relevant to generic optical resonators these $nonlocal$ $maps$ emulate the
basic spatiotemporal phenomena as spatial solitons, vortex eigenmodes breathing
via relaxation oscillations mediated by noise, vortex-vortex and
vortex-antivortex lattices with periodic location of vortex cores. The smooth
multimode noise addition facilitates the selection of stable entities and
elimination of numerical artifacts.
