Terminology

Note

Status: IMPLEMENTED

This page provides brief definitions for evolving terminology within HYWE.

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Hygrid

Orthogonal Cartesian coordinates plus hexagonal adjacency, used as the spatial framework for organizational interpretation and topology generation. See Hygrid Coordinate System for a detailed explanation.

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Lexel

The parsing layer responsible for interpreting relational syntax and architectural programming structures.

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Hexel

The fundamental, indivisible atomic spatial unit of the HYWE universe, anchoring the system to an integer grid.

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Coxel

A formal aggregation of connected Hexels logically grouped around a root Base Hexel, constructed sequentially by a fixed topological operator.

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Goxel

The geometry layer responsible for generating Hygrid-specific geometry, deterministic boundary evaluation, island resolution, and polygon processing for planar configuration.

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Xyxel

The planar spatial configuration layer responsible for 2D organizational interpretation.

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Nexel

The nesting layer responsible for resolving internal spatial recursion and sub-configurations (a Xyxel within a Xyxel).

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Zaxel

The volumetric stacking layer responsible for vertical spatial aggregation and massing (a Xyxel above a Xyxel).

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Hynteract

The data ingestion and dataset structuring framework supporting the capture, pairing, and organization of architectural intent, HYWE Syntax, and deterministic spatial configurations.

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Relational Types

To accurately reason about spatial architecture, HYWE formally distinguishes between different types of relationships:

• Adjacency ($A \sim B$): A physically neighboring relationship between two discrete units (e.g., shared boundaries).
• Connectivity ($A \leftrightarrow B$): A traversable relationship between spaces (e.g., doors, corridors). Adjacency does not imply connectivity.
• Flow ($A \xrightarrow{w} B$): A directed or weighted movement relationship (e.g., expected circulation patterns).
• Visibility ($A \rightleftharpoons B$): A perceptual relationship (e.g., lines of sight between rooms).
• Containment ($A \subset B$): A parent/child spatial relationship (handled via Nexel).
• Hierarchy ($A < B$): A programmatic or organizational relationship (handled via Lexel).