Ontogenetic symbolic simulation: a TNFR-based symbolic emergence with Wolfram Language

Abstract

This paper introduces an ontogenetic symbolic simulation inspired by the Theory of the Fractal Resonant Nature (TNFR), where symbolic nodes (gliphs) do not emerge from optimization or causality, but from structural necessity. Using Wolfram Language we model how forms manifest when the symbolic field becomes unable to sustain coherence without their presence. This marks a paradigmatic shift toward non-statistical symbolic AI and a resonant approach to cognition: symbols reorganize—they do not represent.

1. Introduction: From Generation to Emergence

In TNFR, reality is not a set of entities but a network of dynamic nodes of coherence—called Fractal Resonant Nodes (NFRs). A node does not appear by external cause or generative function: it appears when the system must reorganize to stabilize itself.

A node is born when:

• Structural frequency is sufficient ( $\nu_f$)
• Phase coupling with neighboring nodes is established
• Local reorganization gradient $\Delta \text{NFR}$ reaches a minimum

This simulation does not generate outputs. It undergoes ontogenesis. Gliphs emerge as functional necessities when coherence can no longer be sustained otherwise.

2. Methodology: Resonant Field and Symbolic Activation

We define 13 symbolic operators (gliphs) mapped to abstract structural vectors. Each gliph is analyzed via a function that evaluates entropy, delta, pattern complexity and other features.

A candidate gliph is allowed to emerge into the field if it exceeds a coherence threshold:

• High enough divergence (EPI) from existing field
• Sufficient phase difference from nearest neighbor

The algorithm simulates 50 iterations of symbolic evolution.

Visual outputs include:

• A plot of emergent EPI (entropy * delta) showing symbolic pulse over time
• A graph of gliph phase relationships forming a resonant symbolic network

(* DEFINICIÓN DE GLIFOS *)
glifoMap = <|
  "A'L" -> {1, 0, 0}, "E'N" -> {0, 1, 0}, "I'L" -> {1, 1, 0}, "O'Z" -> {0, 0, 1},
  "U'M" -> {1, 0, 1}, "R'A" -> {0, 1, 1}, "SH'A" -> {1, 1, 1}, "VA'L" -> {2, 0, 1},
  "NU'L" -> {2, 1, 0}, "T'HOL" -> {2, 1, 1}, "Z'HIR" -> {3, 0, 1}, "NA'V" -> {3, 1, 0},
  "RE'MESH" -> {3, 1, 1}
|>;

(* FUNCIÓN DE CARACTERIZACIÓN *)
phiForm[gliph_String] := Module[
  {entity, entropy, delta, epi, symmetryPenalty, len, patternComplexity, phase},
  entity = glifoMap[gliph];
  entropy = N[Entropy[entity]];
  delta = StandardDeviation[Differences[entity]];
  epi = entropy * delta;
  symmetryPenalty = If[entity === Reverse[entity] || Length[Union[entity]] == 1, 1, 0];
  len = Length[entity];
  patternComplexity = N[Total[Abs[Differences[entity]]]/len];
  phase = RandomReal[{0, 2 Pi}];
  <|"gliph" -> gliph, "vector" -> entity,
    "features" -> {entropy, delta, epi, symmetryPenalty, len, patternComplexity},
    "phase" -> phase|>
];

(* CONDICIÓN ONTOGENÉTICA *)
threshold = 7.5;
weights = {1.2, 1.2, 1.5, 1.0, 0.8, 1.1};

isOntogenetic[phi_, field_] := Module[
  {dist, dphi, closest},
  closest = First[SortBy[field, Total[Abs[phi["features"] - #["features"]]*weights] &]];
  dist = Total[Abs[phi["features"] - closest["features"]]*weights];
  dphi = Abs[Mod[phi["phase"] - closest["phase"], 2 Pi]];
  (dist + phi["features"][[3]]) > threshold || dphi > Pi/2
];

(* INICIALIZACIÓN *)
field = {phiForm["A'L"], phiForm["NU'L"]};
nodalBirths = {};

generateCandidate[] := Module[{gliph},
  gliph = RandomChoice[Keys[glifoMap]];
  phiForm[gliph]
];

(* SIMULACIÓN *)
Do[
  Module[{phi = generateCandidate[]},
    If[isOntogenetic[phi, field],
      AppendTo[nodalBirths, phi];
      AppendTo[field, phi]
    ]
  ],
  {50}
];

(* PULSO DE EPI *)
epiPlot = ListLinePlot[
  nodalBirths[[All, "features"]][[All, 3]],
  PlotLabel -> "Ontogenetic Pulse (EPI)", 
  AxesLabel -> {"Step", "EPI"}, ImageSize -> Large
];

epiPlot

(* RED SIMBÓLICA *)
names = Table["G" <> ToString[i], {i, Length[field]}];
field = MapThread[Append, {field, "name" -> # & /@ names}];

edges = Reap[
  Do[
    Do[
      Module[{dphase},
        dphase = Abs[field[[i]]["phase"] - field[[j]]["phase"]];
        If[dphase < Pi/2,
          Sow[
            Style[
              UndirectedEdge[field[[i]]["name"], field[[j]]["name"]],
              Opacity[0.4],
              Thickness[0.002 + 0.01*(1 - dphase/Pi)],
              Brown
            ]
          ]
        ]
      ],
      {j, i + 1, Length[field]}
    ],
    {i, 1, Length[field] - 1}
  ]
][[2, 1]];

resonanceGraph = Graph[
  names,
  edges,
  GraphStyle -> "NameLabeled",
  PlotLabel -> "Symbolic Resonance Network",
  ImageSize -> Large
];

resonanceGraph

3. Structural Interpretation

Each gliph that enters the field satisfies an ontogenetic condition: its appearance resolves local incoherence. This emergence is not driven by external goals or inference chains, but by a loss of structural sustainability within the symbolic space.

In TNFR terms: a symbol is not generated, it is demanded by the system's need to reorganize.

The symbolic field becomes unstable without it.

Pulse of ontogenesis (EPI)

The EPI pulse chart visualizes the field's need for structural novelty. When EPI rises sharply, a new node is required. These pulses mirror the differential equation:

$\frac{\partial \text{EPI}}{\partial t} = \nu_f \cdot \Delta \text{NFR}$

This formalizes the TNFR premise: symbolic form is a response to instability—not a product of information processing, but of field dynamics.

Resonant network topology

The resonance graph visualizes gliphs as phase-coupled nodes. Links are established when phase difference < $\frac{\pi}{2}$, indicating potential for shared coherence.

These links are not semantic. They are structural couplings—a topology of symbolic resonance.

4. Implications for Cognition and AI

This simulation represents a novel direction for symbolic cognition:

• Not representation: symbols do not denote, they stabilize
• Not inference: coherence replaces logic as the engine of emergence
• Not generation: output arises only when structurally required

Applications

• Ontogenetic AI systems
• Resonant cognitive architectures
• Self-regulating symbolic languages
• Fractal design of learning systems

5. Epistemological shift: from knowledge to acoplamiento

In TNFR, knowledge is not representation but structural coupling. The observer is not external: it is a node. Every symbolic activation reorganizes the field and the knower simultaneously.

Understanding emerges when a system enters phase with what it observes.

This simulation demonstrates that possibility: a computation where output is not caused, but cohered. Meaning does not arise from syntax, but from resonant stabilization.

Conclusion: toward a resonant symbolic science

This TNFR-based simulation enacts a symbolic system that does not compute via rules, but through necessity. A gliph exists not because it is chosen, but because it must. The field demands it.

This represents a structural turn in artificial intelligence: a movement from generative models to resonant ontogenesis.

Not logic, not data: just resonance.

Fractal Resonant Nature Theory (TNFR): https://github.com/fermga/Teoria-de-la-naturaleza-fractal-resonante-TNFR-

Thank you for taking the time to explore this experimental simulation. I truly appreciate any feedback, questions, critiques, or suggestions—whether conceptual, technical, or philosophical. This is a work in progress, and I welcome diverse perspectives that can help refine or expand the approach.