For those who equate James Horner with his Oscar-winning “Titanic” score — and many more think of that blockbuster’s signature hit, “My Heart Will Go On,” as a Celine Dion song, even if Horner composed it — a much more rounded portrait of the movie maestro emerged in the wake of his death in a plane crash on Monday.

In terms of social media alone, Horner was remembered as a sensitive, giving, highly versatile composer who was branching out into new territory as a musician before his untimely death at age 61.

In one tweet, Ellen DeGeneres observed: “Think of your favorite music from a movie. Odds are it was composed by James Horner. What an incredible talent. What an incredible loss.”

For every James Cameron blockbuster like “Titanic” and “Avatar” in Horner’s ouevre, there was more character-driven fare like “Searching for Bobby Fischer” and “Iris.”

On Facebook, Robert Townson, head of soundtracks for the Varèse Sarabande label, warmly recalled his time with Horner when the composer was being honored at the annual Hollywood in Vienna showcase in 2013. The label chief and producer pointed out that Horner was “beginning a whole new chapter of his musical life.”

“Since this very special event, James has actually been turning his creativity toward the concert hall,” Townson said in his post. “While still scoring films, he has also composed a double concerto for violin and cello called ‘Pas de Deux’ (2014) and a new concerto for four horns and orchestra called ‘Collage.’ This was a new frontier he was only starting to explore. And films still held limitless challenges.”

At that Viennese event, Horner talked to Townson about his approach to scoring the Ron Howard film “A Beautiful Mind” (2001), about the math genius John Nash. Horner’s score presages Alexandre Desplat’s math-inspired music for last year’s “The Imitation Game.”

“There’s something lovely about this sequence about the beauty of mathematics,” Horner told the audience after they were shown a clip from the film, “and what I was trying to do with the music is create music like a kaleidoscope… The music has no key, the music could just go on forever through all the different keys.”

That heartfelt, complex score — utilizing voices, woodwinds, strings, harp and piano — points to a range of which many were not aware. Horner wore that heart on his sleeve in other ways.

The indie producer-exec Jonathan Dana, also on Facebook, recalled Horner’s gracious contribution to the 1996 Sundance entry “Spitfire Grill.”

“He came to the rescue and did the score for ‘Spitfire Grill’ totally on spec, giving all the money to the 70 local union musicians who performed his magnificent music,” Dana wrote. “He was amazing to watch work, conducing the orchestra without a ‘click track,’ and making modifications to the score, as needed, on the spot! Could not have been more gracious or inclusive, and was more thrilled than anyone at the success of the film and its Sundance Audience Award.”

Other pockets of the Web talked about Horner’s gifts in the most seemingly unlikely places, like the 1992 early cyber-thriller “Sneakers,” work a Variety colleague pointed to as having turned him on to Horner’s gifts as a film composer. Slate reprinted a 2012 appreciation of the film’s music by Nicholas Britell, himself a composer and Juilliard grad who contributed music to such films as “12 Years a Slave.”

“The music in ‘Sneakers’ is hauntingly beautiful and written in a sophisticated and understated manner,” wrote Britell. “But part of what makes the score special is that it doesn’t necessarily sound like what you’d expect for a film in the ‘computer-hacking/spy-game’ genre. It features unlikely elements — choirs, folk themes, minimalist piano, the saxophone of Branford Marsalis — that lend the film an unusual emotional richness and depth. The score does a great job of making you ‘feel’ all of the mysteries that Robert Redford’s Martin Bishop and his merry band of hackers must unravel.”

That emotional richness is something that Oscar-winning songwriter and ASCAP president Paul Williams touched upon in a statement: “James was masterful at creating music that moved us in the most heartfelt ways, with depth and passion.”