Algorithm for drawing a “Squiggly wiggly” pattern

I’m looking to have an algorithm that can randomly draw a “squiggly wiggly” pattern as per the picture.

enter image description here

It would be nice if it were progressively drawn as you would draw it with a pen and if it were based on speed, acceleration and forces like a double pendulum animation might be.

This would be for javascript in the p5 library.

Is there some way of producing this that a) looks hand drawn and b) fills a page, somewhat like a Hilbert curve?

Very interested to hear ideas of how this could be produced, regardless of whether there is some kind of formal algorithm, although a formal algorithm would be best.

Cheers