Gradientilla

Gradientilla is a neologism used in digital design and related discussions to denote a small, controlled gradient—an incremental transition between two values over a short span. The term combines gradient with the Spanish diminutive -illa, signaling a subtlety appropriate for fine-grained changes in color, brightness, or numerical parameters.

Concept and properties: A gradientilla is implemented as an interpolation function f: [0,1] -> [start, end], where t maps to an intermediate value. The key idea is to select an easing or curvature function g(t) that yields a gentle transition, typically monotonic, with limited slope at the ends to avoid abrupt changes. This contrasts with abrupt step changes or large-scale gradients.

Variants: linear gradientilla uses a straight-line interpolation; ease-in and ease-out gradientillas use cubic or quintic polynomials to produce smooth start or end; S-curve gradientillas provide symmetric acceleration and deceleration.

Applications: In color grading and UI design, gradientillas help create perceptually smooth ramps, reducing color banding in low-bit-depth images and improving readability in charts. In data visualization, they can encode continuous values with subtle transitions.

Implementation: Given values a and b and parameter t in [0,1], value = a + (b - a) * g(t). Common choices for g include t, 3t^2 - 2t^3, or 0.5 - 0.5 cos(pi t).

History and usage: The term is not standard in formal mathematics, but appears in tutorials and speculative discussions as a convenient descriptor for fine-grained gradients.