Gay.jl - Wide-Gamut Deterministic Color Sampling

Wide-gamut color sampling with splittable determinism using Pigeons.jl SPI pattern and LispSyntax integration.

bmorphism Contributions

"We are building cognitive infrastructure for the next trillion minds" — Plurigrid: the story thus far

Author: @bmorphism (Barton Rhodes)

Gay.jl embodies the Plurigrid principle of autopoietic ergodicity — self-sustaining systems that explore all accessible states. The deterministic color generation from seeds mirrors the broader pattern of reproducible, verifiable computation across distributed systems.

Related bmorphism projects:

• bmorphism/slowtime-mcp-server - MCP server for time intervals
• plurigrid/act - cognitive category theory building blocks
• Parametrised optics for cybernetic systems

Repository

• Source: https://github.com/bmorphism/Gay.jl
• Author: @bmorphism
• Language: Julia
• Pattern: SplitMix64 → GF(3) trits → LCH colors

Core Concepts

SplitMix64 Determinism

# Deterministic color from seed
using Gay

seed = 0x598F318E2B9E884
color = gay_color(seed)  # Returns LCH color
trit = gf3_trit(seed)    # Returns :MINUS, :ERGODIC, or :PLUS

GF(3) Conservation

Every color operation preserves the tripartite balance:

• MINUS (-1): Contractive operations
• ERGODIC (0): Neutral/balanced operations
• PLUS (+1): Expansive operations

Sum of trits across parallel streams must equal 0 (mod 3).

LispSyntax Integration

using LispSyntax

# S-expression colorization
sexp = @lisp (defun factorial (n) (if (<= n 1) 1 (* n (factorial (- n 1)))))
colored = colorize(sexp, seed=seed)

Integration with plurigrid/asi

With gay-mcp skill

# MCP tool registration with deterministic colors
using Gay, MCP

tool = MCPTool("color-palette", seed=0x1069)
palette = generate_palette(tool, n=5)

With spi-parallel-verify

# Verify GF(3) conservation across parallel execution
using Gay, SPI

streams = trifurcate(seed, [:task1, :task2, :task3])
verify_conservation(streams)  # Asserts sum(trits) ≡ 0 (mod 3)

With triad-interleave

# Interleave three color streams
using Gay, TriadInterleave

schedule = interleave(
    minus_stream(seed),
    ergodic_stream(seed),
    plus_stream(seed)
)

Key Functions

Use Cases

1. Deterministic UI theming - Same seed → same colors everywhere
2. Parallel task coloring - GF(3) ensures balanced distribution
3. CRDT conflict resolution - Trit-based merge ordering
4. Terminal session coloring - vterm integration via crdt-vterm-bridge

Julia Scientific Package Integration

From julia-scientific skill - related Julia packages:

Scientific Domain Coloring

# Protein structure coloring
using Gay, BioStructures
pdb = read("1CRN.pdb", PDB)
chain_colors = Gay.palette(seed, nchains(pdb))
visualize_structure(pdb, colors=chain_colors)

# Quantum circuit coloring
using Gay, Yao
circuit = chain(4, put(1=>H), control(1, 2=>X))
gate_colors = [Gay.color_at(seed, i) for i in 1:length(circuit)]

# Graph neural network visualization
using Gay, GraphNeuralNetworks, GraphMakie
node_colors = Gay.palette(seed, nv(graph))
graphplot(graph, node_color=node_colors)

Related Skills

• gay-mcp - MCP server with Gay.jl colors
• spi-parallel-verify - Strong Parallelism Invariance verification
• triad-interleave - Three-stream scheduling
• bisimulation-game - GF(3) conservation in game semantics
• julia-scientific - Full Julia package mapping (137 skills)

Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

Visualization

• matplotlib [○] via bicomodule
  • Hub for all visualization

Bibliography References

• general: 734 citations in bib.duckdb

Cat# Integration

This skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:

Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826

GF(3) Naturality

The skill participates in triads satisfying:

(-1) + (0) + (+1) ≡ 0 (mod 3)

This ensures compositional coherence in the Cat# equipment structure.