Integer Sequence Font

by Éric Angelini, Erik Demaine, Martin Demaine, Carole Dubois, 2023

Size Color
Interrupt lines at

This typeface represents each letter and digit by a finite sequence of integers, generally between 1 and 19. (As a special exception, spaces use negative numbers.) By combining these sequences together, we can represent any desired text by an integer sequence (shown at the bottom under Sequence).

The sequence is designed to look like the text when plotted or graphed, where the x coordinate is the sequence position and the y coordinate is the integer in the sequence. This is a challenging constraint for font design, because it means that there is exactly one dot at each integer x coordinate. Two types of plots are available: a scatter plot with dots, which makes the text readable; and a line plot, which depending on the line thickness makes the text challenging to read — a puzzle font. Of course, another puzzle font is the integer sequence at the bottom, which requires the reader to make their own plot.

This typeface is inspired by The On-Line Encyclopedia of Integer Sequences (OEIS), created by Neil J. A. Sloane, and recently featured in the New York Times. The OEIS has hundreds of thousands of integer sequences (most of them infinite), serving as a useful resource for mathematicians to discover the names of and equivalences between combinatorial structures.

Using the controls at the top, you can modify the dot size and color of the scatter plot, and the line thickness and color of the line plot, as well as the thickness and color of the axes. If you set any size/thickness to zero, that component disappears entirely. You can also choose to interrupt the line plot at each word or letter boundary, to make the puzzle font a bit easier to read.

Self-graphing sequence. You can use this typeface to make an infinite sequence whose graph gives the sequence itself, because the sequence for “1” starts with 1. Here are the first 5,821 terms. The quest for this sequence, and an early version of this typeface, are described in this blog post by Angelini (in French). This version of a self-graphing sequence used to be part of the OEIS as sequence A343884, but it has since been removed (presumably because it is an object of design, not naturally occurring mathematics). [To see the old A343884 sequence, disable JavaScript to avoid being redirected to the new sequence.]

Check out other mathematical and puzzle fonts. • Feedback or not working? Email Erik. • Source code on GitHub.