# 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:

$x(t) = v*t + {x_0}\,$

where x(t) is the position at any given time, v is the velocity, t is time, and ${x_0}$ is the initial position.

Given initial input values v and ${x_0}$, we can exactly predict the position of $x(t)$ at any time in the future or the past.

## Non-Deterministic System

A non-deterministic system is a system where a single set of inputs can produce multiple outputs; randomness determines future states. If a non-deterministic 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 non-deterministic 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.