Why do Julia sets contain non-periodic points if they're defined by periodic points?

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Kortirion
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I'm a little bewildered when reading about these Julia sets. From the definition a Julia set is the closure of all repelling periodic points of a complex map f.
However I read that a Julia set always contain periodic and non-periodic points. Wasn't the definition including only periodic points? What am I missing here.
 
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The "Julia set" in the second definition is the closure of the "Julia set" of the first definition.