Intermingled basins due to finite accuracy

We investigate numerically first a chaotic map interrupted by two small nei ghborhoods, each containing an attracting point, and secondly a periodicall y tilted box within which disorderly colliding disks can reach different at tracting configurations, due to dissipation. For finite, arbitrarily small accuracy, both systems have basins of attraction that are indistinguishable from intermingled basins: any neighborhood of a point in phase space leadi ng to one attractor contains points leading to the other attractor. A bifur cation destabilizing the fixed points or the disk configurations causes on- off intermittency; the disks then alternate between a "frozen" and a gaslik e state.