Coordinate Encoding for Layered Locations (CELL) Specification

Version: 1.0.0
Author: Sashité
Published: June 17, 2025
License: MIT License

Overview

Coordinate Encoding for Layered Locations (CELL) defines a standardized format for representing coordinates on multi-dimensional game boards using a cyclical ASCII character system. CELL supports unlimited dimensional coordinate systems through the systematic repetition of three distinct character sets.

Game Protocol Foundation

The fundamental game concepts used in this document are interpreted as described in the Game Protocol.

Format Specification

Structure

<dimension-1>[<dimension-2>[<dimension-3>[...]]]

Grammar (BNF)

<cell> ::= <latin-lower> <tail₁>

<tail₁> ::= ε                      ; End after 1D
          | <arabic-numeral> <tail₂>

<tail₂> ::= ε                      ; End after 2D
          | <latin-upper> <tail₃>

<tail₃> ::= ε                      ; End after 3D
          | <latin-lower> <tail₁>  ; Resume new cycle

<latin-lower>   ::= <latin-lower-char>+
<arabic-numeral> ::= <positive-integer>
<latin-upper>   ::= <latin-upper-char>+

<latin-lower-char> ::= "a" | "b" | "c" | ... | "z"
<latin-upper-char> ::= "A" | "B" | "C" | ... | "Z"

<positive-integer> ::= <non-zero-digit> <digit>*
<non-zero-digit> ::= "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
<digit> ::= "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"

Regular Expression

\A[a-z]+(?:[1-9]\d*[A-Z]+[a-z]+)*(?:[1-9]\d*(?:[A-Z]+)?)?\z

Protocol Mapping

CELL encodes multi-dimensional coordinates using a cyclical three-character-set system:

Dimension Type	Character Set	Examples
n % 3 = 1	Latin lowercase letters	`a`, `b`, `c`, `aa`, `ab`
n % 3 = 2	Arabic numerals	`1`, `2`, `3`, `10`, `11`
n % 3 = 0	Latin uppercase letters	`A`, `B`, `C`, `AA`, `AB`

Dimensional Mapping

1D: a, b, c…
2D: a1, b2, c3…
3D: a1A, b2B, c3C…
4D: a1Aa, b2Bb, c3Cc…
5D: a1Aa1, b2Bb2, c3Cc3…

System Constraints

Character Encoding

CELL coordinates use ASCII characters (letters and digits), providing broad compatibility across systems.

Validation Rules

Character validity: Each dimensional component must use only characters from its respective character set
Cyclical consistency: Dimension type must match expected position in the three-character cycle
Order preservation: Characters within each dimension must follow specified ordering
Extension validity: Extended characters must follow systematic repetition patterns
Numeric format: Numeric dimensions must represent positive integers only
Sequential order: All coordinates must begin with dimension 1 and follow strict cyclical progression

Design Properties

Multi-dimensional support: Coordinate systems of any dimensionality
Unique identification: Each coordinate identifies a specific location
ASCII compatibility: Standard character encoding for broad system support
Predictable ordering: Systematic character set rotation
Extensible pattern: Logical expansion through repetition

Implementation

Ruby Reference

Cell.rb – Reference implementation with full cyclical system support and multi-dimensional validation.

Practical Examples

Comprehensive implementation examples across 1D, 2D, and 3D coordinate systems are available in the CELL Examples Documentation.

Relationship to Other Notations

Notation	Purpose	Relationship to CELL
HAND	Reserve location format	Complements CELL by providing `"*"` notation for off-board locations
PMN	Mechanical move decomposition	Uses CELL coordinates for board positions in action sequences
GGN	Movement possibility rules	Uses CELL coordinates for board positions in movement constraints