I want to create simulations such as ecosystems, supply and demand, natural selection, and flight. These projects may be presented visually in a game engine, but I want the underlying systems to represent real concepts rather than simply faking the results.
I have a computer science degree, although I assume I would need additional knowledge in areas such as physics, economics, biology, and mathematics. How deeply do I need to study each subject? Would introductory university textbooks be enough, or would several advanced texts be necessary? Is a foundation in calculus, statistics, and linear algebra sufficient to begin?
I would appreciate a practical list of subjects to study and advice on how to approach learning them while building simulations.
4 Answers
The prerequisites depend heavily on the subject being modeled. A traffic simulation requires knowledge of traffic flow, for example, while an ecosystem requires biology and population dynamics. You usually do not need to master an entire academic field before starting. Pick one domain, research the specific mechanisms you want to represent, and begin with a deliberately simple model. You can increase its sophistication as you discover what matters.
Treat the engine as the presentation layer and keep the simulation logic separate. First decide what assumptions and equations or rules describe the domain, then implement and validate those rules independently. The realism of a simulation comes less from using a particular engine and more from choosing an appropriate model, understanding its limitations, and checking its outputs against expected results.
For many simulations, a useful general mathematics foundation is algebra, basic calculus, probability and statistics, and some linear algebra. The exact balance varies: calculus is important for continuous motion and differential equations, statistics and probability matter for randomness and populations, and linear algebra is central to graphics, spatial transformations, and many physics techniques. Numerical methods and differential equations become useful once you move beyond simple rules.
You do not need to finish several textbooks before writing code. Learn the mathematics required by the next feature, then test the model against known behavior or real data. A computer science background already gives you a good starting point.
Start with a small discrete-time model rather than trying to build a complete world. Define the state of the system, implement one update step or “tick,” and run that step repeatedly in a loop. You can initially print the results instead of creating graphics.
A simple genetic algorithm is a good exercise: represent candidate solutions as arrays of values, combine or mutate them to produce offspring, and evaluate each one with a fitness function. That teaches populations, iteration, randomness, and emergent behavior without requiring advanced biology. Once the model works, add visualization and complexity gradually.

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