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What does unfolding of attractor mean?

Effect of time scales on the unfolding of neural attractors paper talks about Takens embedding theorum. It says that the embedding dimension should be large enough to unfold the attractor. What does the term unfolding of the attractor mean in non technical terminology? What is the significance, why to map the time series to higher dimension when we can work with single time series as higher dimension adds more complexity? An attractor consists of the coordinates of the variables, say Lorenz system. SO the attractor will have 3 coordinates. Then what does unfolding mean?

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