On the Subject of Spectre Maze

Penrose would be proud. For real this time.

On the module there is a prism with a base in the shape of a spectre monotile, with buttons extending from each of the fourteen edges. There will also be glyphs floating on the tile.

Interaction

The left glyphs display the current position, read top down. The right glyph shows the goal position, cycling through the coordinates in order. This feature is only accessible on memory spaces, which will be detailed below.

Hovering over a button will show which edges may pair with the edge corresponding to the highlighted button, in the form of extending the buttons on said edges and retracting any others. If one edge on one tile and another edge on another tile connect, but the edges do not pair, their connection will be considered a wall when encountered in the maze. This feature is only accessible on memory spaces, which will be detailed below.

Pressing any button will transport you to the tile attached via the corresponding edge. If this results in collision with a wall, the current location will not change. It is not recommended to wander outside of the familiar region as the module may behave unpredictably.

To learn more about the current location, you may request new information in the form of a partial memory space by selecting the edges where the tile they lead to cannot yet be determined. Selecting an edge can be done by holding any button for over half a second, which then lets you toggle edges freely. Pressing the tile itself will then submit those edges. Note that more information can only be gathered on the edge of the tiles that can be determined from the coordinates that have already been gathered so far.

Pressing the tile without any edges selected will submit the current location. This location should match its lowest layers with the goal position to solve the module. Any subscript on the uppermost given layer of the goal position will not be considered.

Memory spaces are spaces that give more information than other spaces. These will only appear on the initial position and on any position that has been struck on. Additionally, there are partial memory spaces which display only the information needed to expand the familiar section of the plane by one layer. Both memory spaces and partial memory spaces are permanent, but striking on a partial memory space will convert it to a complete memory space.

Any collision with a wall or any incorrect submission will incur a strike.

Position

Each position is represented by a (technically) infinite sequence of labels. All but the last of these labels refer to a metatile, which is simply an indication of how tiles in the layer below connect to compose it. The last label or coordinate represents a monotile. For each pair of consecutive labels, the former represents the metatile one layer up, which the latter resides in.

In the diagrams below, each monotile (or pair of monotiles in the case of Γ) on the left is paired with its corresponding metatile on the right. On both monotiles and metatiles, one edge has been marked with an arrow, which can be used to determine where the edges are mapped to on higher layers. Note that in the lowest layer, Δ and Σ are connected by an edge of size 0, which is marked as a vertex with a ring. Coincidentally, the arrow for Δ is on this edge.

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The diagrams below (continued)

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The diagrams below (continued)