The study of some typical complex computer simulations, presenting one or more Complexity features, as the: a) symmetry breaking, b) nonlinear properties, c) dissipative processes, d) high-logical depth, e) selforganizing processes, etc allows to point out some several numerical artifacts, namely the: (i) distortions, (ii) scattering, (iii) pseudo-convergence, (iv) instability, (v) mis-leading (false) symmetry-breaking simulations and others. The detailed analysis of these artifacts allowed clarifying the numerical mechanisms of some such artifacts, which can be named in following numerical phenomena, because their basic features can be exactly predicted.

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