Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determined by comparing their results to the real-world outcomes they aim to predict.

Simulation of a system is represented as the running of the system’s model. It can be used to explore and gain new insights into new technology and to estimate the performance of systems too complex for analytical solutions.

Formerly, the output data from a computer simulation was sometimes presented in a table or a matrix showing how data were affected by numerous changes in the simulation parameters. The use of the matrix format was related to traditional use of the matrix concept in mathematical models.

However, psychologists and others noted that humans could quickly perceive trends by looking at graphs or even moving-images or motion-pictures generated from the data, as displayed by computer-generated-imagery (CGI) animation.

Although observers could not necessarily read out numbers or quote math formulas, from observing a moving weather chart they might be able to predict events (and “see that rain was headed their way”) much faster than by scanning tables of rain-cloud coordinates.

Computer simulations have become a useful tool for the mathematical modeling of many natural systemsin physics (computational physics), astrophysics, climatology, chemistry, biology and manufacturing, as well as human systems in economics, psychology, social science, health care and engineering.

Computer simulations are realized by running computer programs that can be either small, running almost instantly on small devices, or large-scale programs that run for hours or days on network-based groups of computers.

The scale of events being simulated by computer simulations has far exceeded anything possible (or perhaps even imaginable) using traditional paper-and-pencil mathematical modeling.

In 1997, a desert-battle simulation of one force invading another involved the modeling of 66,239 tanks, trucks and other vehicles on simulated terrain around Kuwait, using multiple supercomputers in the DoD High Performance Computer Modernization Program.

Other examples include a 1-billion-atom model of material deformation; a 2.64-million-atom model of the complex protein-producing organelle of all living organisms, the ribosome, in 2005; a complete simulation of the life cycle of Mycoplasma genitalium in 2012; and the Blue Brain project at EPFL (Switzerland), begun in May 2005 to create the first computer simulation of the entire human brain, right down to the molecular level.