Section 3.15 Models and Simulations (2026)

Models and simulations are most useful when real-world events are impractical for experiments (e.g., too big, too small, too fast, too slow, too expensive, or too dangerous). Watch the following videos, paying particular attention to the different ways in which the models abstract away certain details from the real world situations that are being modeled. Discuss with your classmates which features of the solar system each model chose to include and to exclude. How do those choices align with the educational goals of each model?

Bill Nye’s Model

Bill Nye illustrates the problem of trying to build a scale model of the solar system by using his bicycle to demonstrate the relative sizes and the relative distances between the planets.

7-Mile Long Scale Model

Starting with an Earth the size of a marble, these folks built a full-scale model of our solar system across 7 miles of Nevada desert.

Second Life 3D Model

This solar system model is built in Second Life, on online virtual world. Think about the differences between this model and the others.

Simulations are used in many fields, including physics, biology, economics, and social sciences. They allow researchers to test hypotheses, explore scenarios, and make predictions about complex systems that would be difficult or impossible to study in the real world.

Computer simulations often use randomness to model real-world events. For example, a simulation of a coin toss might use a random number generator to determine whether the result is heads or tails. This allows the simulation to mimic the unpredictability of real-world events.

Computers cannot generate truly random numbers, but they can generate pseudorandom numbers that are close enough to random for most purposes. Pseudorandom numbers are generated using algorithms that produce sequences of numbers that appear random, but are actually determined by an initial value called a seed. By using different seeds, we can generate different sequences of pseudorandom numbers.

If you perform this experiment, heads will often come up 10 times, but not always, even though, supposedly, the probability of getting a head on a fair coin toss is 50%.

The problem with this experiment is you didn’t perform enough trials to draw any conclusion about the hypothesis that this is a fair coin. You would need to flip the coin many more times to get a better idea of whether the coin is fair or biased. This is where simulations can help.

We have already used the random module in Python to generate random numbers. The random.randint() function can be used to simulate a coin toss by generating a random integer between 0 and 1, where 0 represents heads and 1 represents tails.

Simulations are often used to model population growth. In this simulation, you will explore how populations of rabbits and wolves change over time based on different initial conditions and parameters. You will be able to adjust the birth rates, death rates, and other factors to see how they affect the populations of both species.

This simulation of rabbits and wolves shows how nature attempts to stay balanced. Read the Learner’s Tab about how the simulation works and then complete the following activities. (Note that this simulator works best in the Firefox browser).