geometry - Painting with a Pendulum: Would it be possible to graph the pattern?

I intend to try and replicate an experiment that I found online:

The idea seems to be:

1. Attach a string to a fixed, overhead object


2. Attach a can of paint to the string


3. Put a hole in the bottom of the can and plug it


4. Pull the can to one side


5. Unplug the hole and release


6. The paint can will apparently paint some sort of reducing, Fibonacci spiral

The experiment seems relatively straightforward.

---

However, I'd like to take it one step further:

If possible, I would like to:

1. Ascertain the formula for this line


2. Plug it in to some sort of open-source graphing software


3. Plot on a large-format plotter (mine can print up to 42" wide).


4. Compare the theoretical line to what actually happens in practice (with paint)

Since I would be doing this experiment myself, I think I would be able to determine some of the variables, such as:

1. Volume of the paint can



2. Rate of paint release over time


3. Distance of initial travel from the release point to the natural resting point (would it be an arc?)


4. Other factors?

Question:

What would the formula be for this line?

The catch: I know nothing about math or physics. This would be a learning experience for me, to say the least.