MāyāJīva: Navigating the Magnetic World on MayaLucIA

Analysis: Phase Diagrams and Validation

Wed, 25 Feb 2026 12:00:00 +0100

The analysis framework provides the tools for systematic exploration of the model’s parameter space. It uses a fast vectorised simulation (bypassing per-step ring attractor dynamics) to enable large-scale sweeps: 200 bugs × 100+ parameter points per sweep.

Key Analysis Products

Contrast (singlet yield anisotropy) vs. compass noise → phase boundary separating navigating from lost regimes. The critical contrast threshold (~0.02) determines which radical-pair models support navigation.

Robustness Budget

Suppression mechanisms that reduce compass contrast:

Godot Integration: 3D Interactive Visualisation

Wed, 25 Feb 2026 12:00:00 +0100

The computational core of MāyāJīva is written in C++20 header-only templates. The Godot GDExtension wraps these templates as engine-native nodes, making the simulation inspectable and controllable inside a 3D scene.

GDExtension Nodes

Node	Wraps	Purpose
`BugNode`	`Bug<8>`	Navigating agent in 3D space
`LandscapeResource`	`Landscape`	Magnetic field environment

The BugNode exposes all parameters (compass noise, steering gain, memory leak) as Godot properties, editable in the inspector. The LandscapeResource allows declarative anomaly setup through the Godot editor.

Magnetic Landscapes

Wed, 25 Feb 2026 12:00:00 +0100

The landscape is the world the bug navigates — a 2D magnetic field environment that models the Earth’s geomagnetic field plus geological anomalies. The uniform geomagnetic field provides the compass signal; the anomalies test the compass’s robustness.

Geomagnetic Background

The background field is characterised by:

Declination — the angle between geographic and magnetic north
Inclination — the dip angle (how steeply field lines plunge into the Earth)
Total intensity — ~50 μT at mid-latitudes

An inclination compass (like the radical-pair mechanism) measures the angle between the field and the local vertical, not the field direction. This means it cannot distinguish north from south — it detects the axis, not the polarity.

Path Integration: The CPU4 Circuit

Wed, 25 Feb 2026 12:00:00 +0100

Path integration is the ability to maintain an estimate of displacement from a starting point by accumulating self-motion cues. In desert ants and bees, this is the primary homing mechanism. In Drosophila, the CPU4 neurons in the central complex are believed to perform this computation.

The CPU4 Model

Eight neurons with preferred directions spaced evenly around the circle. Each neuron integrates the component of velocity along its preferred direction:

Input: heading (from ring attractor) and speed (constant in our model)
Accumulation: half-wave rectified projection of velocity onto preferred direction
Memory leak: optional exponential decay parameter λ that causes old displacements to fade
Decoding: population vector gives the home direction; its magnitude gives the distance

The Memory Leak Trade-Off

A perfect integrator (λ = 0) remembers everything but accumulates drift errors on long journeys. A leaky integrator (λ > 0) forgets old displacements, creating a “horizon” beyond which the bug cannot navigate home. This trade-off generates a phase diagram: for each noise level, there is an optimal exploration duration beyond which homing fails.

The Bug Model: Braitenberg Navigation

Wed, 25 Feb 2026 12:00:00 +0100

The bug is a Braitenberg-inspired vehicle that navigates using stochastic Langevin dynamics. It has a position, a heading, and a single steering input derived from its compass circuit. The locomotion model is intentionally minimal: an Euler–Maruyama integrator of heading and position, with rotational diffusion providing the “random walk” that makes exploration possible.

The Locomotion Law

The bug moves at constant speed along its heading direction. Steering is governed by:

Goal-directed torque — derived from the difference between current heading and home direction (from path integrator)
Rotational noise — Gaussian white noise scaled by a diffusion coefficient
Compass input — the ring attractor’s decoded heading, which itself depends on the quantum compass

The balance between deterministic steering and stochastic exploration determines whether the bug can navigate home. This is quantified by the Péclet number — the ratio of directed transport to diffusion.

The Ring Attractor and Quantum Compass

Wed, 25 Feb 2026 12:00:00 +0100

How does an insect brain represent a compass heading? The ring attractor is a neural circuit where activity forms a bump that rotates around a ring of neurons, tracking the animal’s heading. In Drosophila, this circuit lives in the ellipsoid body (E-PG neurons). In our model, it serves as the bridge between quantum chemistry and behaviour.

The Radical-Pair Compass

The compass sensor models cryptochrome — a flavoprotein in the insect eye that forms radical pairs under blue light. The singlet yield of the radical pair depends on the orientation of the Earth’s magnetic field relative to the molecule’s hyperfine axis. This anisotropy is tiny (a few percent) but sufficient for navigation.

MāyāJīva: Navigating the Magnetic World on MayaLucIA

Analysis: Phase Diagrams and Validation

Key Analysis Products

Navigation Phase Diagram

Robustness Budget

Godot Integration: 3D Interactive Visualisation

GDExtension Nodes

Magnetic Landscapes

Geomagnetic Background

Path Integration: The CPU4 Circuit

The CPU4 Model

The Memory Leak Trade-Off

The Bug Model: Braitenberg Navigation

The Locomotion Law

The Ring Attractor and Quantum Compass

The Radical-Pair Compass