Peano curve

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Take the diagonal of a square, as shown on the left in the diagram. Replace this by the nine diagonals of smaller squares (drawn here in a way that indicates the order in which the diagonals are to be traced out). Now replace each straight section of this by the nine diagonals of even smaller squares, to obtain the result shown on the right. The Peano curve is the curve obtained when this process is continued indefinitely. It has the remarkable property that it passes through every point of the square, and it is therefore described as space-filling. Any similar space-filling curve constructed in the same kind of way may also be called a Peano curve.

Subjects: Mathematics.

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