Friday, February 26, 2010

Plot That Movie Plot

Reading Nathan's remark about seeing bits, reminded me of Bill Cheswick's recent off-the-wall project where he (previously of Internet map posters c. 1998) prints movies, frame by frame, using an HP DesignJet 6100ps plotter. Yes, every frame of the movie is literally printed as part of a contiguous whole—which really makes it more of an on-the-wall project, I suppose.

The plotter output shown above is from a 1.36 h animated movie comprising 720 frames per column by 163 columns. Cheswick's original motivation was to hammer the printer but, by considering each of the 117,360 micro-frames to be a color-encoded pixel, it might be possible to detect emergent global structure among the "bits" that is different from the typical story-board structure. However, caution is required because, although all meaning has a pattern, not all patterns have a meaning.

A strikingly similar kind of visualization has been applied to Darwin's Origin of Species, by color-encoding the updated text across all 6 editions. Here, a colored word of text corresponds to a movie frame in the previous example.

In mathematics, visualizing number-theoretic sequences as literal diadic bit-pattens can also reveal hidden global structure.

This is a plot of 2,000 iterations of a certain bit-sequence of the famous 3x+1 problem, that I generated in Mathematica. Each row contains 10 cells that are 16 bits wide by 50 bits deep. The iteration pattern (time series) is slightly different from the previous examples. It is read row-wise from top to bottom in each cell. This could easily be rearranged to be consistent with the above column-wise mappings. Do you see any plot in the plot?