linearpattern

Linear pattern, or linearpattern, is a term used across mathematics, engineering, and computer science to describe a sequence, arrangement, or repetition of elements placed along a straight line with constant spacing or according to a linear rule. It encompasses simple arithmetic progressions as well as practical instantiations in design and programming.

In mathematics, a linear pattern often refers to an arithmetic progression: a_n = a_1 + (n−1)d, where the difference between consecutive terms is constant. In the study of functions, linear functions y = mx + b yield outputs that change at a constant rate, and samples taken at uniform input steps produce evenly spaced points along a line.

In engineering and design, a linear pattern commonly means duplicating a feature along a straight axis. For example, a linear pattern in computer-aided design or manufacturing might copy a hole, notch, or extrusion at fixed intervals. Such patterns can be arranged in a single row or extended to multiple rows guided by a direction and spacing parameter.

In computing and graphics, linear patterns appear when generating arrays or textures by applying a linear rule: position_i = start + i * step, for i from 0 to n−1. This yields predictable, scalable repetition along one dimension.

Limitations include confinement to a single dimension and to linear progressions; more complex layouts may require multi-dimensional patterns or nonlinear spacing.

See also: arithmetic progression, linear function, lattice, replication, tiling.