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.

Terminology

For complete definitions of terms used in this document, see the Glossary.

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

Coordinate System 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

Examples

See CELL Examples for practical implementation guidance.

Reference Implementations

Ruby

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