Explanation About 688

This comic is self-referential, because every graph is dependent on the whole comic. If you were to change anything in the comic, you would change the ink distribution, and would therefore have to update all three graphs. This would result in further changes that would have to be considered.

In the first panel’s pie chart, “this image” refers to the entire comic image, the one that can be downloaded from xkcd (and the entire comic as displayed here above). This is a little confusing as it would be easy to misunderstand this meaning, and believe that the first panel only refers to itself. The title text though makes it clear that it is the entire comic that is called image here. The image size is 740×180 or 133200 pixels. Out of those, 14228 pixels are black (gray pixels are accounted based on their brightness). Ratio of black pixels to the size of the image is 0.1068, so the pie chart segment describing black part should be about 38.5 degrees wide, which is indeed true for the pie chart in the image.

In the second panel the amount of black used in each panel is displayed in a bar chart. This actually makes this panel the one that uses most black. First panel (including the border) has 4944 black pixels, second 6180 and the third 3103. First bar is about 70 pixels high, second about 87 and the third about 43, which roughly checks out. It is hard to measure exact height of the bars as the axis and bars themselves are not straight.

The third panel features a scatter plot labeled “Location of black ink in this image.” It is the first quadrant of a cartesian plane with the zeroes marked. The graph is the whole comic scaled proportionally to fit the axes, so the last panel also has to contain an image of itself having an image of itself ad infinitum thus displaying the Droste effect, a type of visual recursion.

The title text refers to the comic’s own self-reference, but it is also self-referencing because of the character count in it. It would be difficult to write this sentence, as just one more character would not be solved by writing 243, as three has two more than two, and four has only one more…

“The graph of panel dependencies is complete and bidirectional, and every node has a loop.” This means that if we draw a dot corresponding to each panel, and then we draw arrows connecting the dots to indicate dependencies, the resulting graph is complete (meaning that all the points are connected to one another) and bidirectional (meaning that if point A has an arrow to point B, then point B also has an arrow to point A). “Every node has a loop” means that each point also has an arrow connecting to itself.

This is an observation of the interdependent relationship between description and creation that pertains to all things perceived by humans, including the concept of “Self”.

Self-reference was used very early for instance in 33: Self-reference, but never so famously as here. See other self-references here.