title_body: How to model the change of script over time
upvoted_answer: The surface that things are written on. Runes were carved in trees and, as such, do not have curves. The Greek alphabet was written on tablets, and curved lines were possible. The Arabic alphabet was written quickly on papyrus. Also, some civilisations might prefer cursive script over others. Arabic letters differ whether they're isolated, at the beginning of a word, at the end or in the middle. So does your handwriting with the Roman script. But Arabic kept their cursive when the digital age came, and the Roman script got rid of it and created the same character.
  Os (runes), psi (Greek alphabet, but modernised on a computer, see footnote 1), šīn (Arabic script, isolated)
  
  ᚩ, Ψ, ش
  Let's call the ancestor A. The two daughter languages will be called B1 and B2. A could be a pictographic script, from which B1 devised a syllabary but B2 kept pictographs. Or A was an abjad (alphabet without vowels) and B1 became an alphabet whereas B2 stayed an abjad.
  Although language is passed on from mother language to daughter language with diachronics, script doesn't need to. In fact, you don't often see one script in the same language for three language-generations except in some cases like Latin (but Vulgar Latin wasn't really written much). Borrow a script from a neighbouring language. This is what I recommend doing.
  
  
  
  
  Footnotes: 1) Ancient Greek part of the Rosetta stone. Greek characters in Unicode are in many fonts modernised, this is an example of typical Ancient Greek script.