We describe the construction of an N-body simulation that mimics the true velocity and mass-density fields in a box of side 256\hmpc about the Local Group , and the production of mock catalogs that mimic in detail current catalogs of redshifts and peculiar velocities. Our main purpose is to provide a tool for developing and testing reconstruction methods, but the different components of the method can be used on their own in other applications. The initial conditions are based on the IRAS 1.2Jy

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... redshift survey, assuming that galaxies trace mass and \Omega=1. A density field smoothed is recovered from the redshift survey, using quasi-linear theory and a power-preserving filter. The corresponding potential field is traced back to the linear regime using the Zel'dovich-Bernoulli equation. Small-scale power is added by means of constrained realization to mimic fluctuations on galactic scales. The gravitating system is evolved forward in time with a PM code of 2\hmpc resolution. The result reproduces the real dynamical structures on large scales and the statistical properties of the structure down to galactic scales. "Galaxies" are identified via a linear biasing scheme (b=1.35) and they are divided into "spirals" and "ellipticals" to obey Dressler's morphology-density relation. The galaxies are assigned internal-velocity parameters and absolute magnitudes scattered about an assumed mean Tully-Fisher relation. They are then "observed" as magnitude-limited samples, trying to mimic the selection criteria of the data sets constituting the Mark III catalog of peculiar velocities. Artificial IRAS 1.2Jy redshift surveys are also compiled. The simulations and mock catalogs will be made available electronically as bench marks for testing reconstruction methods.