Glossary

12-point solution
A selection of the four ignotiles (butterfly, strider, box, and windmill) such that all possible diagonal lines are used in their construction. Also known as an ignoquad.

Basic Shapes
The five different shapes that make up the ignotiles: triangle, left- and right-handed parallelograms, trapezoid, and sphinx.

Boundary dissolving (merging)
Any one of several rule-based techniques for dissolving boundaries between shapes in adjacent ignotiles in order to create new "merged" shapes. For example, first we can merge the central square in a tile with parallelograms or trapezoids to get a "bridge" shape (image on left, below). Then we can follow some rules to merge more shapes: 1) never dissolve diagonal lines, only horizontal or vertical; 2) Merge bridge shapes first; 3) Once bridge shapes have been merged, merge other shapes that share an edge. 4) Shapes may not have self-intersections. The resulting shape is shown on the right, below, colored according to other rules.

Finite Projective Plane
Non-rigorous definition: An N x N array of N different elements selected into ordered sets of N-1 elements such that all sets are unique and all set elements at position k (k < N) form Latin squares.

Four-color Solution
A coloring solution for the ignoquads in which exactly four colors are assigned to the basic shapes in an ignotile according to a set of rules and no two adjacent shapes have the same color.

Greco-Latin Square
An N x N array of N unique pairs of different elements such that no element repeats in any row or column and both the first and second elements in each pair form Latin squares.

Latin Square
An N x N array of N different elements such that no element repeats in any row or column.

Ignoquad
A 2 x 2 array of tiles that form a 12-point solution.

Ignosquare
A 4 x 4 array of ignotiles, 16 tiles selected from a possible 32, where no tile repeats in an any row, column, or quadrant, and each quadrant is a 12-point solution (ignoquad).

Ignotile
One of four graphic elements used in algorithmic compositions, referred to as the butterfly, strider, box, and windmill. Each tile has eight rotations and reflections. Thus there are 32 ignotiles arranged in eight groups of four.

Permutations
Systematic reordering of a sequence of different things. In mathematics, a permutation of N objects is any one of the N! (factorial N = N x N-1 x N-2 ... x 3 x 2 x 1) possible sequences of the N objects taken N at a time. Ignoring reflections and rotations, there are 24 possible permutations of the ignotiles.

Shading Rule
A rule for changing the value (but not necessarily the chroma or color) of a shape, group of shapes, or area of an algorithmic composition. A very common shading rule in the ignotiles is to shade one diagonal half of the tile, as shown in the set of 24 permutations of the tiles.