- 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.
- 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.
- 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.
- 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.
- An N x N array of N different elements such that no element repeats in any row or column.
- A 2 x 2 array of tiles that form a 12-point solution.
- 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).
- 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.
- 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.
- 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.