Does the calculation of this transaction fee follow any consistent pattern or general rule? Could you perhaps illustrate it with a concrete example?
The tx fee is proportional to tx size. And tx size is determined by the number of inputs and outputs.
For a normal tx sent to one recipient plus your change address (so 2 recipients) what matter the most is the number of inputs.
Let's say it's more expensive to spend a bag full of cents than spending an 100$ bill.
In Electrum you can do View->Show Coins and then in the coins tab you can see your
(currently unspent) inputs and the addresses they are residing in.