This communication presents a two decades-updating on different applications of a new simulation method using simplex rule for smoothing regulation processes of several cooperative or competing components of complex mixture systems in biology and chemistry. Application fields covers different matter scales varying from atomes to ecosystems via molecular and biological organism levels. Simulation results issued from simplex approach helped for better understanding (i) inter-atomic regulation ways of molecular synthesis, (ii) organization metabolic pathways from chromatographic data, (iii) feeding behaviors of multi-prey foraging animal species. Application perspectives of the simplex machine-learning method are widely opened for highlighting multidirectional and multiscale regulation processes of polymorphism and diversification of multi-cluster complex systems from big data satisfying mass conservation principle.