Theory - akilmarshall/procedural-image-generation GitHub Wiki

$\mathbb{I}$ denotes a tiled image, that is an image composed of a tile sheet also known as a tile set.

$\mathbb{T}$ denotes the tile sheet of $\mathbb{I}$,

\mathbb{T} = \{t_1, t_2, \cdots{}, t_n\}

each tile set $\mathbb{T}$ contains $n$ items each denoted $t_i$ where $1\leq i \leq n$.

Neighbor Function

Each image $\mathbb{I}$ also has an associated neighbor function,

    \mathcal{N}_{\mathbb{I}}::t\to d\to \left[t\right],

that takes a tile and a direction and returns a list of the tiles seen adjacent in the specified direction $\mathbb{D}=\{0, 1, 2, 3\}$.

Tiled Image Statistics

Together $(\mathbb{I}, \mathbb{T}, \mathcal{N})$ can be called tiled image statistics (TIS).