Deterministic system
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Lorenz Attractor 
Definition
A deterministic system is a system where an initial state completely determine the system's future states. Thus, there is no randomness in producing the future states. If a deterministic system is given some initial inputs, the model will produce the same states every time.
A very simple example would be a position function:
where x(t) is the position at any given time, v is the velocity, t is time, and is the initial position.
Given initial input values v and , we can exactly predict the position of at any time in the future or the past.
NonDeterministic System
A nondeterministic system is a system where a single set of inputs can produce multiple outputs; randomness determines future states. If a nondeterministic system is given some initial inputs, the model will produce a different state for each run.
Throwing a dice and recording the number it lands on is a nondeterministic system. If the dice is thrown, we will not be able to predict its outcome. If it has been thrown five times and landed on 6 every time, we will still not be able to determine the outcome of the next roll.