A space-filling curve is a continuous mapping from a one-dimensional space to a multi-dimensional space that completely fills the multi-dimensional space, typically a unit square or cube. They are used in various fields to optimize data locality and improve the efficiency of algorithms that require spatial data processing.

Space-filling Curve

space-filling curve

Continuous mapping refers to a function between two topological spaces where the pre-image of every open set is open, preserving the notion of 'closeness' in the spaces. This concept is fundamental in topology and analysis, ensuring that small changes in input result in small changes in output, thus maintaining the structure of spaces under transformation.

continuous mapping

one-dimensional space

multi-dimensional space

unit square

Unit cube

Data locality refers to the practice of processing data close to where it is stored to minimize latency and improve performance in computing systems. By optimizing data placement and access patterns, data locality enhances efficiency in distributed systems and parallel computing environments.

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