by Erik Demaine and Martin Demaine, 2017
The Voronoi diagram of a set of points (called sites) decomposes the plane into cells, one for each point/site, according to what points are closest to that site than any other site. Equivalently, if you light a fire or grow a bacteria simultaneously from all the sites, then the cells are where each fire/bacteria goes, and the Voronoi diagram is where they meet each other.
We offer two typefaces are based on the Voronoi diagram. • In the “Voronoi typeface”, the sites are arranged so that the Voronoi diagram looks like a letter or numeral. Here we rely on hiding (dashing) all Voronoi edges that go off to infinity (or more precisely, that exit the square frame). In this case, we obtain a puzzle font by hiding the Voronoi diagram, and just showing the sites; to decipher the letter/numeral, you have to compute the Voronoi diagram. • In the “Inverse typeface”, the sites themselves are arranged to form the letter or numeral. In this case, the Voronoi diagram becomes the puzzle font: to decode the letter, you must reverse engineer what sites would produce this Voronoi diagram. This problem can be solved in polynomial time; see also the related case of allowing additional sites.
There are several font variations for you to play with. • You can display each letter as a separate Voronoi diagram (as originally designed), or combine them into one big Voronoi diagram via the One diagram checkbox. • You can show/hide the sites and/or the Voronoi diagram, in particular to produce puzzle fonts. • You can color cells with random colors. When enabled, you can choose the range of allowed hue, saturation, and lightness using the sliders. For example, tighten the hue range to approach single-color tilings; lower the maximum saturation to 0 to make grayscale; or increase the lightness range to simulate stained glass. In the Voronoi font, you can use Separate glyph cells to choose different ranges for cells that constitute the font's glyphs. Tap on a cell (outside Draggable mode) to reroll its color. • You can toggle visibility of the grid that the sites were designed on. • Draggable mode lets you play with modifying the letters by dragging the points around, and having the Voronoi diagram dynamically update. (Outside this mode, letter Voronoi diagrams are precomputed.) All changes are temporary, and will be reset if the text or font change. The Reset button will also reset all changes. • The slider allows you to scale the size of the letters/numerals.
These fonts were designed in our custom Voronoi Designer webapp. Try making your own letters! You can play with our font designs here: • Voronoi typeface: • Inverse typeface:
Our 2021 paper “More than Words: Fonts as Generative Art” explores making art prints and tilings using these fonts. This is when we added the “one diagram” and coloring features.
Check out other mathematical and puzzle fonts. • Feedback or not working? Email Erik. • Source code on GitHub.