cinemagraph
n. A still image where an element or small area of the image has been animated.
Examples
2012
But the coolest GIFs as of late have come from the rise of Cinemagraphs, where creators take an image and animate one aspect of it, looping it together seamlessly to create an illusion of video where there is none—the image of a woman's skirt ruffling in the wind, or of a taxi seen in a reflection, driving past a café window.
—David Mendez, “Show Us Your GIFs!,” Tucson Weekly, December 13, 2012
2012
These days Gifs range from small, repeating film grabs embedded into blogs as a sort of illustrative punctuation, to the spectral Cinemagraphs of Jamie Beck and Kevin Burg.
—Tim Dowling, “Gifs: the retro animations that just won't die,” The Guardian, August 26, 2012
2011 (earliest)
Les tendrils.
—Kaelen Haworth, “Cinemagraphs,” Ann Street Studio, February 12, 2011