Julia Sets: Periodic and Non-Periodic Points Explained

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Julia sets are defined as the closure of all repelling periodic points of a complex map, yet they also contain non-periodic points. This duality can cause confusion, as the initial definition seems to focus solely on periodic points. The inclusion of non-periodic points arises from the iterative nature of complex maps, where the behavior of points can change over iterations. Essentially, the second definition refers back to the first, expanding the understanding of Julia sets. Clarifying these concepts is crucial for comprehending the full structure and behavior of Julia sets in complex dynamics.
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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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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