Abstract: This post introduces a symbolic-structural simulation inspired by the Fractal Resonant Nature Theory (TNFR), a paradigm where physical systems are not made of objects, but of dynamically stable resonance nodes. Using Wolfram Language, we visualize how local interactions lead to emergent global coherence. A direct export to GIF is also included.

1. Theoretical background: from particles to nodes

TNFR proposes that the basic unit of reality is not matter or fields, but nodes of structural resonance (Nodos Fractales Resonantes, or NFRs). Each node is defined by:

• A structural frequency ( $\nu_f$)
• Phase alignment with neighboring nodes
• A coherence gradient ( $\Delta NFR$)

Core equation: $\frac{\partial EPI}{\partial t} = \nu_f \cdot \Delta NFR$

Where $EPI$ (Primary Information Structure) is not passive information, but a dynamically sustained zone of vibrational coherence.

2. Simulation goal

We simulate the emergence of coherence from noise, representing a symbolic-structural model of nodal organization. Over time, disordered states self-organize into patterns, mirroring TNFR’s notion of ontogenesis nodal.

3. Code: animated coherence emergence + GIF export

(* Seed chaotic field *)
seed = RandomReal[{0, 1}, {40, 40}];

(* Evolution function with local averaging + noise *)
evolve[state_] := Module[{new},
  new = Table[
    Module[{neigh, avg},
      neigh = state[[Max[i - 1, 1] ;; Min[i + 1, Length[state]],
                     Max[j - 1, 1] ;; Min[j + 1, Length[state[[1]]]]]];
      avg = Mean[Flatten[neigh]];
      Clip[0.6*state[[i, j]] + 0.4*avg + 0.02 RandomReal[{-1, 1}], {0, 1}]
    ],
    {i, Length[state]}, {j, Length[state[[1]]]}];
  new
];

(* Generate 50 evolution steps *)
frames = NestList[evolve, seed, 50];

(* Show animation inside notebook *)
ListAnimate[
  ArrayPlot[#, ColorFunction -> "Rainbow", Frame -> False, ImageSize -> Medium] & /@ frames,
  AnimationRate -> 2,
  DefaultDuration -> 10
]

(* Export to GIF (Wolfram Cloud compatible) *)
CloudExport[
  ArrayPlot[#, ColorFunction -> "Rainbow", Frame -> False, ImageSize -> 300] & /@ frames,
  "GIF",
  "evolucionTNFR.gif"
]

4. Interpretation

• Each frame shows a step toward increasing coherence.
• Structures stabilize locally through recursive interaction.
• No external designer is needed: order emerges from vibration.

5. Some applications and inspiration

• Complex systems modeling
• Symbolic AI / cognition
• Bio-inspired computing
• Artistic generative design

For non-programmers: what is this doing, and why it matters (TNFR context)

Imagine starting with a canvas full of random colored dots — pure chaos. What this program does is:

1. Makes each dot adjust to its neighbors at each step.
2. Adds a little randomness so it doesn’t become too uniform.
3. Repeats this process over time.
4. As you watch, you see order gradually emerging: color zones stabilize, patterns appear.

This is a visual metaphor for a key idea in the Fractal Resonant Nature Theory (TNFR):

• Reality is not made of things, but of coherences that sustain themselves.
• Each pixel is like a node trying to find phase with others.
• When they do, a resonant structure appears — this is what TNFR calls ontogenesis nodal.

You are not just seeing pretty colors. You’re watching the birth of form from vibration — no external controller, just local interactions building global coherence.

Reference

• Fractal Resonant Nature Theory (TNFR): https://linktr.ee/fracres — The theory is written in Spanish, but its symbolic logic and vibrational framework can be explored interactively in any language. This GPT assistant, called Manual simbiótico de coherencia estructural, is trained specifically on TNFR and available at https://chat.openai.com/g/g-z0wzRk9ju-manual-simbiotico-de-coherencia-estructural.)

Closing thought: This simulation is more than a pattern generator. It is a visual grammar of becoming — a resonant unfolding of structure from noise, as theorized by TNFR. Feedback and collaboration welcome!