The first idea that came into my mind upon seeing this prompt was exactly exemplified by the above image: a dilemma. A split path. A difficult choice. Maybe even a chasm or schism.
These are all rather metaphorical interpretations. As is my next thought - the notion of 'splitting hairs'.
This led me to perhaps more literal - but no less evocative - possible developments of this prompt. What if you dropped something precious on the floor and it broke into two pieces? What would that look like? How would you feel? Could you repair it? Would you want to? Would it still be the same object if you did?
And now I'm getting philosophical again. Sorry about that.
I'm going to suggest something rather obscure - the Anglo-Saxon riddle - purely for its highly visual split down the middle.
Don't worry - nobody expects you to write in Anglo-Saxon!
The most famous Anglo-Saxon riddles are located in the Exeter Book. Unsurprisingly located in Exeter, UK, specifically in Exeter Cathedral. And who spent three years studying ENGLISH LITERATURE, OF ALL THINGS, in Exeter and never ONCE went to see it? *points at self* (...yep. Kick me now.)
I've been informed by someone with a master's in literature from Cambridge, and former education professor, that the gaps in the riddles occur at each line's halfway point - and each half-line is alliterative. So the split is not just visual - which for our purposes is very convenient.
But I understand if you don't feel up to writing a riddle. After all, the ones in the Exeter Book are so complex that many scholars have spent years unravelling them. If nothing else, Megan Cavell's British Library article on the subject makes an entertaining read that it would be a shame for you to miss out on.
With most of my ideas and images above seeming to necessitate action or resolution, I leave you with Abraham Lincoln:
In the meantime, read other participants' poems, share the #octpowrimo hashtag on social media, and add your link to your own poem in the comments below.