The sine function produces smooth repeating variance usable as a custom noise alternative

Sine (sin) and cosine (cos) return values between -1 and +1 that vary smoothly and periodically as their angle argument increases. Unlike Perlin noise, sine is fully deterministic and periodic (repeats exactly every 2π radians). This makes it useful as a controlled variance function: y = baseY + sin(angle) * amplitude produces a smooth wave. Composing sine with itself — cubing it (pow(sin(rad), 3)) or mixing with noise — breaks the regularity and produces more complex, less obviously periodic curves. The key insight is that mathematical transformations of simple functions can approximate unpredictability without a noise function.

Examples

Sine curve: y = 50 + (sin(radians(angle)) * 40); — a classic sinusoidal wave. Sine cubed: y = 50 + (pow(sin(rad), 3) * 30); — sharper peaks and flatter troughs. Sine cubed plus noise: y = 50 + (pow(sin(rad), 3) * noise(rad*2) * 30); — breaks the periodicity.

Assessment

Sketch by hand the approximate shape of y = sin(x), y = sin(x)^3, and y = sin(x)^5 for x from 0 to 2π. Explain why raising to higher odd powers pushes the curve toward the extremes.