In The Girl Who Leapt Through Time, Makoto's aunt is restoring a painting. We find out that Chiaki came from an apocalyptic future only to look at it. But why? What makes this painting anything special?
I felt there were a LOT of things which the director left for us to fill and one of my questions was the same as your's. One of the hair ripping questions that is.
But I feel, that the painting at first was the only reason for him to use his power to travel back in time and no other initiatives in mind, of course until he met Makoto which had a huge impact in life.
I feel something massive occurred in his life, and that painting was the centre of this event and he kept the painting very close to his heart even though he did not see it, but it could've been something someone else had seen and then passed away and maybe asked him to see the beautiful artwork for himself. Or maybe looking how dear that painting was to that particular person who was no more with him. IT COULD'VE EVEN BEEN MAKOTO, but that whole time gap between Makoto and Chiyaki still is a mistery to me and everyone else, heck who knows if they even MET.
In my opinion, I believe the producer intended to create a symbol that would significantly remind its viewers about the events that took place in the movie and the meaning behind it.
This is because, I'm looking for a copy of the painting for my wall. I loved the idea of waking up every morning to be reminded of how precious time is.
Thanks the thoughts on this question! I think that the painting represents time and memory too! The fact that it both "travels" backward and forward in time and links and connects people and events.
The lack of direct evidence from the writers and directors allows us to speculate about the relationship to characters and narrative. I believe this is the intention of the anime and the manga in particular.