This puts a big constraint on the kind of physics you can have in a simulation. You need this property: suppose some physical system starts in state x. The system evolves over time to a new state y which is now observed to accuracy ε. As the simulation only needs to display the system to accuracy ε the implementor doesn't want to have to compute x to arbitrary precision. They'd like only have to compute x to some limited degree of accuracy. In other words, demanding y to some limited degree of accuracy should only require computing x to a limited degree of accuracy.

Let's spell this out. Write y as a function of x, y = f(x). We want that for all ε there is a δ such that for all x-δ<y<x+δ, |f(y)-f(x)|<ε. This is just a restatement in mathematical notation of what I said in English. But do you recognise it?

One problem is that the function f(x) is seldom known exactly. In physics, we usually have a differential equation that f is known to satisfy. Actually computing f is another problem entirely. Only in rare cases is the exact solution known. In general, these equations are solved numerically. For a system that evolves in time, you'll pick an increment. You take the initial data at t_0 and use it to approximate the solution at t_1, then use that to approximate the solution at t_2, and so on until you go as far out as you need. At each step you introduce an error and a big part of numerical analysis is figuring out what happens to this error when you take a large number of steps.

It's a feature of chaotic systems that this error grows exponentially. Even a floating point error in the last digit has the potential to rapidly grow and come to dominate the calculation. In the words of Edward Lorenz:

Chaos: When the present determines the future, but the approximate present does not approximately determine the future.