The definition of a pattern that repeats itself is recurring and the correct term is recurrence. This can also be said to be monotonous
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If a pattern repeats itself, it is considered periodic. Periodic patterns follow a predictable sequence of elements that repeats at regular intervals.
Blues music repeats itself in a specific 12 bar harmonic pattern.
You really shouldn't be looking for the answer of a test or homework on the computer. But the answer is How often a wave occurs is the waves frequency.
If you mean the repeating pattern from left to right that occurs in the Periodic Table of the Elements, it is called the Law of Octaves. This is because the pattern of periodicity occurs in groups of eight.
It is The Periodic Table of Elements
The properties of elements that follow a pattern that repeats every eight elements are known as the periodic properties. These properties include atomic radius, ionization energy, electron affinity, and electronegativity, which exhibit periodic trends across periods (rows) in the periodic table.