Tupper's self-referential formula

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Tupper’s self-referential formula is a mathematical inequality that produces a visual representation of itself when graphed over a particular region of the 2D plane. It is a well-known example of the relationship between mathematics, binary encoding, and graphical representation. The formula creates the self-referential appearance due to the choice of an integer that encodes the image. The formula acts as a decoding mechanism, determining whether individual points belong to the plotted image by examining the binary digits of that integer. When the constant is selected appropriately, the resulting collection of points forms a bitmap of the formula itself. A numerical value can encode a sequence of binary digits, those digits can represent a two-dimensional arrangement of pixels, and a mathematical inequality can determine which pixels appear in a graph. The resulting image is therefore an example of a graphical representation whose visual content is stored in a number and recovered through...

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