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Can you see the light? That is, can you see the patterns in light bulbs that are left on, after repeatedly following a simple rule to switch them on and off?
Explore the surprising variations in conceptually simple sequences of numbers, constructed by applying one of two operations to generate each successive term. Can you make the sequence return to its starting value?
Fold a long strip of paper in half several times. Can you see a pattern in the creases formed along the length of the paper? What sorts of route do we trace if we use the creases to direct our turns along a path?