The authors study the `micro chaos' map \(F:x \to ax - b\text{Int} (x)\), describing the local dynamics of a digitally controlled unstable system, being subject to a linear effect of sampling and a nonlinear effect of round-off. These effects frequently cause chaotic oscillations on a microscopic scale near the equilibrium. The authors prove the existence of a hyperbolic strange attractor for a large set of parameter values of the map \(F\) and study its domain of attraction -- being of full measure but possibly having a fractal boundary. Finally, they describe the dynamics on the fractal attractor using symbolic dynamics.