Generating random SVG arrow shapes

Question

So I have a task, which intends to generate random SVG images of curved entangled arrows.

Here are few examples of the expected output:

Example 1

Example 2

Example 3

There are few main requirements:

1. Arrow shape shouldn't have any sharp curves, for example like this
2. Arrowhead should always watch upwards at the end or at least tend to do so
3. Shape starts on the left side of canvas and ends up in the right part
4. There should be a random number (from 1 to 5) entanglements

What would be the best approach for this given that my knowledge of geometry is very basic? Is it even possible to generate random shapes with such requirements?