Butterfly-Shaped Maze

A maze in a silhouette

The passages are carved inside a butterfly-shaped mask of two wings and a body, not into a rectangle. Cells outside the outline do not exist at all, so the maze is the shape. It is not a square maze with a butterfly printed over it.

Thirty cells across by default. A solution page prints after it unless you turn it off.

How it is generated

A recursive-backtracker carve, bounded by the mask. From a starting cell it walks to a random unvisited neighbour, then does it again, and again, reversing whenever it hits a dead end.

The result is a perfect maze: exactly one path between any two points, no loops anywhere, nothing unreachable. It also gives long winding corridors instead of the short branching ones that some other algorithms produce, and that difference is most of why a backtracker maze feels like a maze rather than a grid of choices.

The shape changes the difficulty

Not only decoration.

A rectangular maze has a uniform texture, and an experienced solver works it systematically from one edge. A silhouette does not. It has narrow regions — the body, the wing tips — where the passage count falls to one or two and the geometry forces a channel, so the maze acquires a rhythm: open sections where you have to choose, pinch points where you cannot.

It also makes the maze harder to solve backwards from the exit, which is the standard shortcut.

Setting the resolution

Thirty is a reasonable adult puzzle. Drop to fifteen or twenty for a young child, where finishing is the point rather than being challenged by it.

Raising it makes the passages narrower rather than the maze longer in any interesting sense, and past a certain point the constraint becomes pencil width rather than reasoning. Print at 100% and on A4 at least; a shape maze reduced to fit is a maze nobody can draw a line through.

Where it suits

Spring and summer topics, minibeast work, life-cycle lessons. Party bags, rainy afternoons. It suits anyone who finds a plain grid maze unappealing, and that is a fair number of children.

Colouring the wings afterwards is the obvious extension and worth mentioning to a class, since it turns a five-minute activity into a twenty-minute one.

Related

The maze generator for rectangular mazes at any difficulty, and the math maze if you want the route to depend on getting sums right.