Good point! Here's two OpenGL animations across multiple 1-dimensional vertices:
Perlin- https://i.imgur.com/ROww6bw.gif Random- https://i.imgur.com/EurTdaZ.gif
Perlin- https://i.imgur.com/ROww6bw.gif Random- https://i.imgur.com/EurTdaZ.gif
(By manipulating the available variables in a Bezier curve.)