RAM : Relational Automata Manifolds

RDG–MFE–Q: Generalized Cellular Automata

A strict extension of Conway’s Life, Wolfram CA, graph CA, asynchronous CA, and constrained CA

This repository contains the theory, proofs, demos, and minimal Python implementations showing how RDG–MFE–Q strictly generalizes classical cellular automata by adding:

• RDG — generative relational geometry
• MFE — field‑based dynamics (Life-like, Maxwell-like, PDE-like)
• Q — admissibility, SID stability, quotienting

Classic CA appear as the degenerate case:

CA ≃ (Γ_fixed grid, f_lookup table, Q_∅)

RDG–MFE–Q provides geometry, dynamics, and admissibility as separate, composable layers.

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Future Repository Structure

CA-Extensions-RDG-MFE-Q/
│
├── README.md
│   ├── Overview
│   ├── Classic CA → RDG–MFE–Q Reduction
│   ├── Why RDG–MFE–Q Strictly Generalizes CA
│   ├── Glider Embedding Theorem
│   ├── Emergent Geometry Demo
│   └── Maxwell–Quaternion Appendix
│
├── theory/
│   ├── RDG_MFE_Q_CA_Generalization.md
│   ├── Universality_Theorem.md
│   ├── Emergent_Manifolds.md
│   └── Maxwell_Quaternion_Appendix.md
│
├── rdg/                     # Geometry layer
│   ├── rdg_generators.md
│   ├── rdg_relations.md
│   └── rdg_examples.md
│
├── mfe/                     # Field-dynamics layer
│   ├── mfe_life.md
│   ├── mfe_maxwell.md
│   └── mfe_pde_extensions.md
│
├── q_layer/                 # Admissibility / SID / quotienting
│   ├── admissibility_axioms.md
│   ├── SID_stability.md
│   └── quotienting_rules.md
│
├── code/
│   ├── rdg_mfe_q_minimal.py
│   ├── rdg_mfe_q_life_exact.py
│   ├── rdg_mfe_q_glider_preserved.py
│   └── utils.py
│
├── examples/
│   ├── glider_exact/
│   ├── glider_preserved/
│   └── emergent_grid/
│
└── LICENSE

Domain Papers (Science → 511.3 Cellular Automata)

This project is linked to the CA reference archive:

511.3 Cellular Automata — Domain Papers
https://github.com/JDRedding/Domain-papers/tree/main/500–599%20Science/511.3%20Cellular%20Automata