Complex spatial-temporal dissipative structures occur in shocked porous material. The system is globally in nonequilibrium. Both the simulation and data analysis for such a system are challenging.The system was simulated by using the material-point method which was developed recently. The Minkowski functionals were introduced to describe the Turing pattern of the map of state variable like temperature.The relevance among the three Minkowski functionals,the area fraction of the high-temperature regions and the distribution of "hot-spots"  in space was pointed out.The shock wave reaction with inhomogeneous material was studied by analyzing the evolution of Minkowski functionals. The effects of porosity and shock-wave-strength were investigated.