Aperiodic
Elementary
We say that something occurs aperiodically if the length of time between each time it happens is not always the same.
High school
A function, signal, or sequence of events is aperiodic if the time it takes to repeat varies, so that a shift by any fixed time $T > 0$ changes it.
Undergraduate (real-time systems)
A sequence of times $t_1$, $t_2$, $t_3$, … is called aperiodic if there does not exist a constant $P > 0$ such that
\[t_{i + 1} - t_{i} = P \quad \text{for each } i = 1, 2, 3, \dots.\]Examples
Non-examples
Things that may be mistaken for examples.
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A clock that chimes every hour
Elementary
The chimes of a clock that chimes every hour are sporadic, with minimum separation of one hour, so they are not aperiodic.