  In this paper we present an extremely simple structure solution method termed
charge flipping. It works ab initio on high resolution x-ray diffraction data
in the manner of Fourier recycling. The real space modification simply changes
the sign of charge density below a threshold, while in reciprocal space the
modification is the Fobs map without any weighting. We test the algorithm using
synthetic data for a wide range of structures, analyse the solution statistics
and check the quality of reconstruction. Finally, we reconsider mathematical
aspects of the algorithm in detail, showing that in this chaotic iteration
process the solution is a limit cycle and not a fixed point.
