a non-linear re-interpretation of a given work or media […] combining fragments of various works.
A re-edit is a new version made by cutting-up and splicing together chunks of the original song in a different order, usually using a tape recorder, a razor blade and some sticky tape.[…]If you think of re-editing as making a patchwork version, then remixing is where you actually separate the individual sonic fibres of a song and weave them back into a new piece of musical fabric.
from the book “Last Night a DJ saved my Life”, p 192-193
A remix may also refer to a non-linear re-interpretation of a given work or media other than audio such as a hybridizing process combining fragments of various works. The process of combining and re-contextualizing will often produce unique results independent of the intentions and vision of the original designer/artist. Thus the concept of a remix can be applied to visual or video arts, and even things farther afield.
A remix in art often takes multiple perspectives upon the same theme. An artist takes an original work of art and adds their own take on the piece creating something completely different while still leaving traces of the original work. It is essentially a reworked abstraction of the original work while still holding remnants of the original piece while still letting the true meanings of the original piece shine through.
Remix culture, sometimes read-write culture, is a society that allows and encourages derivative works by combining or editing existing materials to produce a new creative work or product.