This article features the precursors of electronic imaging who worked in avant-garde film and video. It looks at numbers and screen geometry in the early abstract work of Hans Richter and Viking Eggeling, agreeing with Malcolm Le Grice that Diagonal Symphony (1925) was the first programmable artist's film. It traces this lineage through to Len Lye's abstract color montage in the 1930s and to the systematic permutation of words and images in the structural film during the 1970s. These are linked to the new digital abstraction explored by contemporary artist filmmakers in the US and Europe. The article argues for a tradition of frame-based thinking for the screen that anticipates the computer, to assert an independent experimental approach to the shapes and structures generated by the classic film avant-gardes. Rees' main concern was to show the continuing lineage of abstract film into the digital age, as an alternative to the rise of projected video for the gallery, a theme he has also addressed in recent essays for books awaiting publication by Manchester University Press and by Tate Britain. This essay is expanded to full length from a short 2001 version in POINT journal. It contains a wholly new section on contemporary Austrian and UK film and video artists. It also has comprehensive footnotes on both historical and recent films, and is illustrated with a different selection of images. This version dates from a paper given at a conference on avant-garde film held at the University of Edinburgh in September 2004, although publication was delayed by the sudden death of the organiser Dr Scheunemann in 2005. It is published in a series of books by Rodopi on aspects of the European avant-gardes. The other 22 contributors include Maureen Turim, Nicky Hamlyn, Inez Hedges, Pierre Sorlin, William Wees and Yvonne Spielmann.