Schelling's Model of Segregation, developed in 1971, was used to help explain why segregation might be so hard to combat. http://nifty.stanford.edu/2014/mccown-schelling-model-segregation/
This is an agent-based model, where each household or person is an agent that abides by certain rules. As we step through the model, we can witness the dynamics of the model as these rules cause agents to behave in particular (rule-based) ways throughout each simulated step.
I first came across this model in the University of Michigan Coursera course, Model Thinking: https://www.coursera.org/learn/model-thinking/lecture/1qEBU/schellings-segregation-model
The Wikipedia article's opening line definition is: An agent-based model (ABM) is one of a class of computational models for simulating the actions and interactions of autonomous agents (both individual or collective entities such as organizations or groups) with a view to assessing their effects on the system as a whole. https://en.wikipedia.org/wiki/Agent-based_model
Or in other words, using micro or individual level behavior to discover macro or group-level larger scale system behavior.
Personally, I find these problems very fascinating because of the larger (often unintuitive) patterns that arise from individual behavior, where individuals (or agents) act within the bounds of certain rules (not unlike our patterns in real life). Of course, as the set of rules, possibilities, and outcomes (and the combinations and interactions of these rules, possibilities, & outcomes) grow, we end up with a computationally intensive problem, that may even be entirely incorrect due to the reason that it is not unheard of for us to look over, forget, or omit vital rules or bounds needed to appropriately simulate a problem.
Nevertheless, these models can still be fascinating and useful and I hope this application can be at least one of the two.