[2][1] Many techniques exist, including the use of hex editors to manipulate certain components of a compression algorithm, to comparatively simple methods.
[1] Michael Betancourt has posed a short set of instructions, included in the Signal Culture Cookbook, that involves the direct manipulation of the digital file using a hexadecimal editing program.
Some effects produce optical analogues: adding an echo filter duplicated elements of a photo, and inversion contributed to the flipping over of an image.
The similarities result from the waveforms corresponding with the layers of pixels in a linear fashion, ordered from top to bottom.
[1] Ahuja and Lu summarized the process through a quote by Adam Clark Estes of Gizmodo as "the internet's code-heavy version of graffiti.