To undulate means to move in a smooth, wave-like motion, rising and falling in gentle curves. Picture how a snake moves across the ground, its body flowing in S-shaped curves, or how a dolphin's body moves through water. That graceful, rippling motion is undulation.

You can see this kind of motion everywhere. Fields of wheat undulate in the wind, creating rolling waves of golden grain. Sand dunes in the desert have undulating surfaces, with curves and valleys shaped by the wind. When you skip a stone across water, you see undulating ripples spread outward in perfect circles.

Dancers sometimes move with undulating motions, letting their arms or bodies flow smoothly rather than moving in sharp, rigid ways. Swimmers doing the butterfly stroke undulate through the water. Even sound waves and light waves undulate, though you need special equipment to see those patterns.

The word suggests something continuous and rhythmic, not jerky or random. A flag doesn't undulate when it snaps in a strong wind, but it does when a gentle breeze makes it roll and flow. Undulating hills rise and fall across the landscape in smooth, connected curves rather than jutting up in steep, jagged peaks.