Spiral Galaxies Font

by Walker Anderson, Erik Demaine, and Martin Demaine, 2018

 


In a Spiral Galaxies puzzle, you are given a grid of unit squares and a collection of centers (points, drawn as dots). The goal is to decompose the grid into regions called galaxies, one containing each center, so that each galaxy is a polyomino (an edge-to-edge joining of unit squares) and 180° rotationally symmetric about its center.

Spiral Galaxies or Tentai Show (天体ショー in Japanese) is one of the many pencil-and-paper puzzles designed for the Japanese puzzle magazine and publisher Nikoli, Like most Nikoli puzzles, Spiral Galaxies is NP-complete, meaning that there is no efficient algorithm to solve them, assuming P ≠ NP.

This typeface features 36 uniquely solvable Spiral Galaxies puzzles, one for each numeral and letter of the alphabet. The puzzle font shows just the centers. Like the Spiral Galaxies puzzles published by Nikoli, the centers are drawn with dots of two different colors, black and white; after solving the puzzle, the corresponding galaxy polyomino should be filled the same color. The black galaxies then form a letter or numeral. The solved font illustrates these solutions. See our paper for details, including how we designed the typeface.

In the puzzle font, you can try your hand at solving the puzzles by clicking on grid edges to toggle whether they are edges of the galaxy (black). If you Enable third “connected” state, then you can click on an edge a second time to make it gray and perpendicular to indicate that the two connected grid squares belong to the same galaxy. (See Figure 3 of our paper.) The galaxies will fill in when you solve the puzzle. Click Reset all puzzles to start over.

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