arcgrowth

Arcgrowth is a term used in various disciplines to describe growth processes that unfold along or within an arc-shaped constraint. In mathematical modeling, arcgrowth refers to growth characterized by polar coordinates, where a radius r is expressed as a function of angle θ, leading to spiral-like expansion. Common forms include r = a + bθ, which generates an Archimedean spiral, or r = k e^{bθ}, yielding a logarithmic spiral; these forms illustrate how growth can accumulate along a curved path rather than in a purely radial or linear fashion.

In biological contexts, arcgrowth is used metaphorically to describe patterns where development proceeds along curved templates, such as veins or the edge of a leaf following an arc, or in tissue engineering models that constrain growth to arc segments.

In computer science and optimization, arcgrowth may describe algorithms that expand feasible regions along circular or angular directions, or growth-based strategies that prioritize states on a curved boundary, often in path planning or computer graphics applications.

Origin and usage: Arcgrowth is not a single, formal theory but a descriptive term applied in diverse fields. When used, it typically denotes growth constrained to an arc, a spiral trajectory, or a segment of a circle, and can be implemented with polar coordinates or arc-length parameterization.

See also: spiral growth, growth models, polar coordinates, Archimedean spiral, lamination patterns.