When simulating a chaotic system, using different rounding for the floating point values will affect the simulation by a small amount, which a chaotic system is

When simulating a chaotic system, using different rounding for the floating point values will affect the simulation by a small amount, which a chaotic system is liable to amplify. Quantisation of reality seems to be analogous to rounding floats, in the sense that it affects the precision of the measurements. I'd be interested to know whether that affects the "running" of the system like with floats in a simulation, or if it only puts a limit on how well the initial conditions can be defined.