Crate fractal_algebra 

Fractal Algebra & Generative Systems

fractal_algebra is a Rust library for exploring generative art and complex systems through the lens of algebraic structures and quantum-inspired concepts.

The core idea is to represent complex patterns as FractalField objects, which behave like elements in a vector space. These fields can be generated, mutated, and evaluated through an evolutionary process managed by the GeneratorCriticLoop.

This library integrates My original research concept of a FractalGraph enriched with quantum-inspired amplitudes, making it the foundational data structure for advanced simulations within an EntangledSystem.

Key Components

• FractalField: The central data structure, representing a collection of geometric GraphEdges. It supports algebraic operations like addition and scalar multiplication.
• Generator & Critic Traits: A flexible system for creating and evaluating FractalFields. Use EvolutionaryGenerator and CriticSuite for a standard setup.
• GeneratorCriticLoop: An engine that drives the evolutionary process, iteratively finding better fields based on critic scores.
• Resonance Trait: An abstraction for measuring coherence, harmony, and other emergent properties of fractals and their transformations.
• FractalGraph: A semantically-typed, directed graph that serves as the substrate for quantum-inspired computations and particle simulations.
• AI & Bayesian Search: Modules like ai and bayes provide tools for probabilistic searches and simulations within an EntangledSystem.

Example Usage

use fractal_algebra::{
    GeneratorCriticLoop, EvolutionaryGenerator, MutationSuite, CriticSuite,
    SymmetryCritic, EntropyCritic, FractalField
};

// 1. Set up a generator with mutation strategies.
let generator = EvolutionaryGenerator {
    mutations: MutationSuite::new(), // Add strategies here
    count: 10,
};

// 2. Set up critics to evaluate the fields.
let mut critics = CriticSuite::new();
critics.add_critic(SymmetryCritic, 0.7);
critics.add_critic(EntropyCritic, 0.3);

// 3. Create and run the evolutionary loop.
let loop_engine = GeneratorCriticLoop {
    generator,
    critic_suite: critics,
    iterations: 100,
};

if let Some(best_field) = loop_engine.run() {
    println!("Found a best field!");
    // Further analysis on best_field...
}

Re-exports

pub use constants::MODULUS;

pub use field::FractalField;

pub use fractaledge::FractalEdge;

pub use graphedge::GraphEdge;

pub use signature::FractalSignature;

pub use vec3::Vec3;

pub use graph::FractalGraph;

pub use graph::FractalGraphEdge;

pub use graph::EdgeType;

pub use graph::GraphError;

pub use graph::NodeId;

pub use criticloop::GeneratorCriticLoop;

pub use critics::CriticSuite;

pub use evolutionary::EvolutionaryGenerator;

pub use looprep::LoopReport;

pub use mutation::MutationSuite;

pub use rfg::RandomFieldGenerator;

pub use ai::EntangledSystem;

pub use ai::EntropyPulse;

pub use ai::FeedbackSignal;

pub use ai::ParticleResonance;

pub use ai::ProbabilisticSearch;

pub use bayes::FrequencyBeliefSpace;

pub use bayes::Gaussian;

pub use atom::FractalAtom;

pub use resonance::Resonance;

pub use resonance::ResonanceFilter;

pub use resonance::ResonanceLaw;

pub use resonance::ResonantTransform;

pub use resonance::TransformResonanceLaw;

pub use filters::FilterTrace;

pub use filters::LawFilter;

pub use filters::PredicateFilter;

pub use filters::ScoreFilter;

pub use traits::CollectionMember;

pub use traits::Critic;

pub use traits::EntropyCritic;

pub use traits::Fractal;

pub use traits::FractalClone;

pub use traits::FractalCollection;

pub use traits::Generator;

pub use traits::HasSignature;

pub use traits::IFS;

pub use traits::Mandelbrot;

pub use traits::MutationStrategy;

pub use traits::Operation;

pub use traits::SymmetryCritic;

pub use time::Evolvable;

pub use time::FractalSpacetime;

pub use time::SpacetimeCoordinate;

pub use laws::test_associativity;

pub use laws::test_distributivity;

pub use testkit::canonical_test_fractal;

Modules

ai

Defines the core traits and data structures for the quantum-inspired AI system.

atom

Defines the FractalAtom, a fundamental building block representing a value with semantic context.

bayes

Implements a probabilistic search strategy using a Bayesian-like update rule.

constants

Defines global constants used throughout the application.

criticloop

Provides a generator-critic evolutionary loop for finding optimal FractalFields.

critics

Defines a system for evaluating and scoring FractalField instances.

evolutionary

Defines a Generator that uses an evolutionary strategy to create new FractalField candidates.

field

Defines the FractalField struct, a collection of GraphEdges that represents a state in the simulation space.

filters

Defines a comprehensive filtering system for Fractal objects and SemanticUnits.

fractaledge

Defines FractalEdge, an abstract representation of a connection or interaction.

graph

A semantically-typed, directed graph optimized for modification and traversal.

graphedge

Defines GraphEdge, a struct representing a directed edge in a geometric space.

laws

Defines functions for testing the algebraic laws of FractalField.

looprep

Defines the LoopReport struct for storing results from an evolutionary run.

mutation

Defines a system for applying weighted, stochastic mutations to a FractalField.

resonance

Defines the core concepts of Resonance for the Fractal Algebra library.

rfg

Defines a Generator that produces FractalFields with random properties.

signature

Defines FractalSignature, a condensed summary of a FractalField’s properties.

stochastic

Defines a MutationStrategy that applies stochastic jitter to amplitude and phase.

testkit

Provides shared utilities and data fixtures for use in tests.

tests

Contains unit tests and algebraic law verification functions.

time

A conceptual model for a fractal spacetime that can evolve through different states.

traits

Defines the core traits and architectural patterns for the library.

vec3

Defines a simple 3D vector struct (Vec3) and its associated mathematical operations.

Macros

test_vector_space_axioms

A macro to test that a FractalField satisfies basic vector space axioms.