Geodesic Topology

The spatial substrate that enables stable, distortion-free planetary simulation.

The geodesic topology is the foundation of E.D.E.N.’s world representation.
It replaces traditional grid-based approaches with a seamless, equal-area, geodesic sphere composed of tiles, edges, and directed edges.

This topology ensures that spatial relationships remain consistent everywhere on the planet.

Purpose

The purpose of the geodesic topology is to provide a mathematically coherent surface on which all simulation systems operate.
Unlike square grids or lat-long projections, geodesic surfaces minimize distortion, maintain uniform adjacency, and support natural diffusion and flow.

This gives the engine a stable substrate for scientific and emergent systems.

Core Principles

  • Equal-Area Geometry — tiles maintain near-uniform area across the entire sphere.
  • Consistent Adjacency — gradients and flows have stable neighborhood relationships.
  • No Poles or Seams — global phenomena behave naturally around the entire sphere.
  • Direction-Aware Flow — directed edges support asymmetric processes.
  • Subdivision-Based Resolution — higher resolution can be achieved without changing topology.

System Model

The topology consists of:

Tiles

Discrete polygonal regions (mostly hexagons, with exactly 12 pentagons).
Represent scalar or categorical data.

Edges

Boundaries between two tiles.
Represent symmetric relationships (slopes, adjacency magnitudes, boundaries).

Directed Edges

Cardinality: two per edge (A → B, B → A).
Represent asymmetric processes such as flow, transfer, or influence.

Uniform Subdivision Levels

LOD levels increase resolution with consistent geometry.

How It Interacts With Other Systems

  • Field System reads/writes tile/edge/directed-edge data.
  • Tick Engine schedules updates across the surface.
  • Subsystems map their domain logic onto the topology.
  • Overlays visualize tile and edge-based states.
  • Application Layer uses topology for user interaction and inspection.

What This Enables

  • stable environmental modeling
  • global diffusion without seams
  • consistent climate, hydrology, and geology behavior
  • reliable AI navigation and pathfinding (future)
  • natural vector-field visualization
  • scalable resolution for research or gameplay

Visual Examples (Optional)

  • geodesic mesh overlaid on planet
  • tile-centric and edge-centric renders
  • emergent scalar fields mapped across topology

Public Extensibility Notes

Future SDK features may allow developers to:

  • sample tile neighborhoods
  • compute gradients
  • analyze adjacency patterns
  • create custom surface-bound simulations

Topology remains stable and does not change across extensions.

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