Bill Gordon's maze
A teacher (at Rough Rock in Arizona) drew this laborious maze on graph paper to keep the children amused on the last day of term.

Sac maze
I solved it by coloring "sacs"—areas filled by paths leading to dead ends—so as to leave the "through-path" clear.

The maze comes to look like a map of a palace, with mosaic-tiled rooms and courtyards.

Bill Gordon's maze 2
He tried to frustrate my scheme.

("Oh my!" was a surprisingly bland and old-fashioned English exclamation that Navajo kids seemed to like.)

Sac maze 2
Sacs may take the form of islands, surrounded by parts of the through-path.

The sac-and-throughpath analysis can be a tool for improving mazes. It becomes easy to see that no one would bother to enter the large sac just before the exit. By opening or closing entrances between a sac and the throughpath, or between sacs, one can enlarge sacs, re-route the throughpath, generally enhance the paradoxical properties of the maze. And—

Code maze
It struck me that this can be applied as a way of composing mazes. And as a code: draw an outline picture, disguise it by filling each area with a sac of mazy lines; someone else can solve the maze by coloring the sacs and thus reveal the picture. There could be better examples.

Maze of the planets
I later met the maze-maker Adrian Fisher, where he lived at St. Albans in England. During our talk he gave me, on a scrap of paper, this design for a maze embodying the traditional symbols of the eight planets. It has, in elegant form, many of the paradoxical features of an excellent maze. I printed it along with my Daedalus-and-Icarus picture in Astronomical Calendar 1997.

Coming from outer space, you enter through the symbol for Neptune (with his trident) and find your way laboriously inward through the symbols for Uranus, Saturn, Jupiter, Mars, Earth, and Venus—crossing each time, like a looping Pioneer or Voyager spacecraft, almost to the opposite side of the solar system—till at last from Mercury's bedazzled door you enter the court of the Sun.

Lenore maze
Diagram of my low-hedge maze in a garden in Greenville, South Carolina. The plan grew from mowing the lawn spirally. Some of the materials were holly, yew, privet, nandinas, sunflowers, mint, bugloss — it was a template into which to plant anything. There was a wall of massive Leyland cypresses at the right, and I added some as a tongue at the front right. The first false turning led to a compost bin; the second, to a tiny raised lawn. Some passages were blocked by mere "plugs" of ornamental grass. In mazes, there should be plenty of mismatch between geometry and topology. There was an elliptical inner region—geometrical, not topological: its boundary (a front curve of junipers and a rear curve of sections from a fallen maple) was pierced by openings. The innermost region had a herb garden in front of the bench and a trellis behind. Getting to the center necessitated an at first unnoticed path that (with a side outlet to a street) rambled away (under an old swing-set covered by a Carolina jasmine) into a wilderness of brambles and poison ivy. A stick gate closed a way out for the mower.

Daedalus ascending — flying free from the labyrinth he had designed so cunningly that, it was said, he almost became lost in it himself. He had built it for King Minos of Crete, a tyrant who then imprisoned him in it to make sure he would not create such wonders for anyone else. Being a clever craftsman (as Greek daidalos means) he did not need to dig a tunnel but fashioned wings.

I made this sketch in 1996 for a newsletter advertizing an Amnesty International party to be held in the garden (croquet on the bumpy lawn, then a treasure-hunt to the center of the maze).