A reproducible
starting point.

# Phyllux Geometry Lab v1

Educational planar geometry, not a medical device, electrical model, implant design or neural recording system. No clinical, cross-talk or security benefit is claimed. This is newly written educational material, not a private invention implementation or patent document.

## Reproduce

Use Python 3.9 or newer, without extra packages or network access. Run: python geometry_lab.py --output results

The script exports CSV coordinates, editable SVG figures and JSON calculations. Checks verify point count, radial extent and the stated minimum pairwise distance. Parameters can be changed in the functions; the CLI exports the default 121-centre example.

## Definitions

Golden angle = pi*(3-sqrt(5)) radians. For n=0..120: r(n)=3*sqrt(n/120) millimetres; theta(n)=n*golden_angle. There are 121 centres and a maximum lateral radius of 3 mm. Lateral radius is not cortical depth. Minimum centre separation is 0.2738612788 mm, while mean nearest-centre separation is about 0.456659 mm. These are different measures. Electrode size, substrate, wiring, fabrication and actuation are unspecified.

The square reference is an 11 by 11 grid inscribed in the same radius-3-mm circle. Its minimum separation is about 0.424264 mm. It occupies less of the disk; this is not an equal-area or equal-density comparison and cannot support a claim that one layout has better device performance.

The CSV files identify index, x_mm and y_mm. The SVGs show those calculated positions and a scale. JSON records geometry only. Golden-angle/Vogel placement is established mathematical background, not an invention claimed by this lab.

## Useful next work

Review the definitions, add disk-filling reference layouts, choose fair metrics before inspecting results, and reproduce the calculation independently. Electrical behaviour, tissue compatibility, cross-talk and clinical benefit need separate modelling, testing and qualified review. No human-use or implantation instructions are provided.

## Licences and credit

Prepared for David E. Sproule / Phyllux Innovation Commons, 30 October 2026. New code: GPL-3.0-only; full text in LICENSE-CODE.txt. New guide and figures: CC BY-SA 4.0, https://creativecommons.org/licenses/by-sa/4.0/legalcode . Retain credit and identify changes. Existing upstream open licences are not revoked. No private controller, cryptographic algorithm, filing paper or clinical data is included. Distributed modifications follow the applicable licence terms.