Morton number

In mathematical number theory and computer science, a Morton number is a single integer value constructed by interleaving the bits or digits of one or more source numbers. This is often useful for constructing a single hash index from a pair (or more) of input numbers.

In number theory, Morton numbers are useful in proofs, often in examples which map multiple dimensions to one, or vice versa. For example, an infinite 2D grid of integer coordinates can have a single unique Morton number computed for each coordinate, and those Morton numbers give a one-to-one mapping of the infinite 2D coordinates to a 1D coordinate, proving that the infinite number of integer pairs has the same cardinality as the integers.

Number Theory

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