Gaussian Width

The normal (Gaussian) distribution centered at zero is the bell-shaped density \frac{1}{s\sqrt{2\pi}} e^{-x^2/(2s^2)}, where the standard deviation s sets the spread. Here s animates between 0.3 and 2: as it grows the bell widens and its peak drops — the area underneath stays fixed at 1 — and as it shrinks the curve spikes into a tall, narrow concentration. This single-parameter family underlies the central limit theorem and is the maximum-entropy distribution for a fixed mean and variance; sliding s is the most direct way to feel how variance reshapes a distribution while conserving total probability.