Gait Emergence

A walking rhythm appears from field dynamics alone — no central pattern generator, no walk command, no rhythm code anywhere.

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The Question

Where does rhythm come from, if no part of the nervous system is a rhythm generator?

The Answer, Short Version

The field. A shared neuropeptide-bath medium couples the body's four ganglia, and when excited by stimulus it oscillates as it settles toward its attractor. Give each ganglion opposite-sign output legs, and the oscillation is a gait. The walking rhythm is what the field does naturally when pushed away from rest.

The Setup

The tardigrade has four ganglia — G1 anterior, G4 posterior — each driving one pair of legs (La, Lb) with opposite-sign outputs. A shared shared field carries drift across all four ganglia. There is no central pattern generator, no oscillator module, no timing signal, and no "walk" command anywhere in the code.

The test: feed a constant bilateral stimulus, log the leg activations at each timestep, and look at what the legs do. If the field alone cannot produce a gait, leg outputs will drift to some static equilibrium or to uncoordinated noise. If the field can produce a gait, we should see paired alternation (La and Lb opposite signs) and a biologically plausible anterior-to-posterior amplitude wave (G1 loudest, G4 quietest).

What Emerged

Within fifteen timesteps the system resolved to a clean walking pattern:

Step | Field  | G1 → G2 → G3 → G4             | Leg pairs (head → tail)
-----|--------|-------------------------------|-----------------------------
  0  | +0.161 | -0.00 → +0.00 → -0.00 → +0.00 | near-zero
  4  | +0.686 | +0.22 → +0.21 → +0.21 → +0.20 | [+0.22,-0.22] ... [+0.19,-0.19]
  8  | +1.047 | +0.31 → +0.26 → +0.27 → +0.24 | [+0.30,-0.30] ... [+0.24,-0.24]
 12  | +1.285 | +0.31 → +0.25 → +0.26 → +0.22 | [+0.30,-0.30] ... [+0.22,-0.22]
 16  | +1.435 | +0.27 → +0.20 → +0.22 → +0.17 | [+0.26,-0.26] ... [+0.17,-0.17]

Leg pair alternation: 100% Anterior → Posterior wave: YES

Two features, neither programmed:

1. Paired alternation. Every leg pair (La, Lb) has opposite signs at every timestep. This one is the output structure of each ganglion — one leg pushes, one pulls — but the synchronisation of this alternation across all four pairs is a field-coupling effect. Without the shared field, the four ganglia could phase-drift independently. They do not.
2. Anterior-to-posterior amplitude wave. G1's output is consistently larger than G4's — the excitation attenuates as it travels through the shared field. By step 16 the amplitude ratio is roughly 1.5:1 from head to tail. This matches the walking gait of real tardigrades, where front legs do more of the work.

Baseline is also worth noting. With no stimulus at all, the system left to drift already shows the same alternation: [+0.21, -0.21, +0.21, -0.21, +0.22, -0.22, +0.20, -0.20]. The field's resting dynamics already carry the seed of the rhythm. Stimulus doesn't cause the gait; it amplifies and organises something the geometry was already doing.

What This Proves

A single dynamical system — a shared field coupled to four opposite-sign output pairs — produces a walking rhythm without any rhythm-generating component. No central pattern generator. No timing circuit. No oscillator. No walk command. No training loop.

The implication for the VINE paradigm is direct: if you have a field and a body plan with opposite-sign outputs, you do not need to build a rhythm module. Rhythm is what the field does. You get coordinated locomotion for free from the same geometry that handles phototaxis, concept formation, and every level of the tower above.

What This Does Not Prove

This is not a biological claim about how real tardigrade nervous systems generate gait. Real animals have central pattern generators, proprioception, and mechanical feedback that this model does not include. The claim is narrowly architectural: in a system built on shared-field coupling and opposite-sign ganglionic outputs, gait emerges as a natural consequence of the geometry. Whether biology arrived at the same solution is a separate question this experiment cannot answer.

Nor does it claim the gait is optimal, stable under perturbation, or robust to damage. Those are later tests. What it shows is the minimal case: geometry under excitation, walking falls out.

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Raychell Langan · NEXICOG Ltd · Hampshire, UK