Here’s a link to a commentary on the finale of Fringe. The author of this essay focuses on the symbolism of this flower as a message of forgiveness and love.
I agree, although I am very wary of using God-language to describe the nature of the cosmic dynamics at play here. I’d like to add that Fringe expresses a belief that the arts—especially music—have the ability to do more than represent ideas. This simple drawing of a tulip possesses enough permanence and life-altering hope that the characters involved were able to take really big risks for the sake of human life. The material permanence of the tulip transcended space and time in much the same way as a miracle-working icon might defy conventions of how art is made and viewed. Seeing the simple flower helped key characters make decisions that reversed the nightmarish mutations of their future lives.
Music is what helped Walter be more human. He found music helped him deal with overwhelming complexities in his mathematical calculations, it guided him to navigate the murky depths of grief and despair, and it was what he needed to bring him back to himself when the calculated coldness of the dystopian future threatened to annihilate him and the rest of the rag-tag band of resistance.
Music—and all the arts—helped Walter recognize the richness of being human. The lesson he learned was about valuing the emotional and unpredictable dimensions of life, and not seizing rational control of it. Listening to music (and, by extension, engaging with all the arts) pushed him and the rest of his small circle of family and friends to try and understand its forms and meanings. Art makes us more human.
These musings lead me to interrogate another adage. Will beauty save the world? Listening to, seeing, and sensing the arts in all its permutations cause us to seek understanding of its forms and meanings. Asking those questions about meaning and beauty causes us to behave as though we have a life-altering hope in the meaningfulness of life. For Walter and the rest of the Fringe-world, beauty and aesthetic experiences are enough in themselves to soothe troubled souls and motivate characters to make dramatic sacrifices for the sake of loving relationships. In other words, the only world worth saving has beauty.