Crate amari_automata 

Amari Automata

Cellular automata, inverse design, and self-assembly using geometric algebra. This crate implements the mathematical foundation for Cliffy-Alive’s self-assembling UI system, where geometric algebra provides natural composition rules for CA cells.

Key Concepts

• Geometric CA: Cellular automata where cells contain multivectors
• Inverse Design: Finding seeds that produce target configurations using dual numbers
• Self-Assembly: Polyomino tiling with geometric algebra constraints
• Cayley Navigation: CA evolution as navigation in Cayley graphs
• Tropical Solving: Using max-plus algebra to linearize discrete constraints

Architecture

The crate combines three mathematical frameworks:

1. Geometric algebra for spatial relationships and rotations
2. Dual numbers for automatic differentiation through time
3. Tropical algebra for constraint solving and optimization

Usage

use amari_automata::{GeometricCA, Evolvable};
use amari_core::Multivector;

// Create a 2D geometric cellular automaton
let mut ca = GeometricCA::<3, 0, 0>::new_2d(64, 64);

// Set initial configuration with multivector cells using 2D coordinates
ca.set_cell_2d(32, 32, Multivector::basis_vector(0)).unwrap();

// Evolve the system
ca.step().unwrap();

Re-exports

pub use cayley_navigation::CayleyGraph;

pub use cayley_navigation::CayleyGraphNavigator;

pub use cayley_navigation::CayleyNavigator;

pub use cayley_navigation::DefaultCayleyNavigator;

pub use cayley_navigation::Generator;

pub use cayley_navigation::GroupElement;

pub use geometric_ca::CARule;

pub use geometric_ca::CellState;

pub use geometric_ca::GeometricCA;

pub use geometric_ca::RuleType;

pub use inverse_design::Configuration;

pub use inverse_design::Target;

pub use inverse_design::InverseCADesigner;

pub use inverse_design::InverseDesigner;

pub use inverse_design::Objective;

pub use inverse_design::TargetPattern;

pub use inverse_design::TropicalConstraint;

pub use self_assembly::Assembly;

pub use self_assembly::AssemblyConfig;

pub use self_assembly::AssemblyConstraint;

pub use self_assembly::AssemblyRule;

pub use self_assembly::Component;

pub use self_assembly::ComponentType;

pub use self_assembly::Polyomino;

pub use self_assembly::SelfAssembler;

pub use self_assembly::SelfAssembly;

pub use self_assembly::Shape;

pub use self_assembly::TileSet;

pub use self_assembly::UIComponentType;

pub use self_assembly::WangTileSet;

pub use tropical_solver::ConstraintType;

pub use tropical_solver::SolverConfig;

pub use tropical_solver::TropicalExpression;

pub use tropical_solver::TropicalSolver;

pub use tropical_solver::TropicalSystem;

pub use ui_assembly::Layout;

pub use ui_assembly::LayoutConstraint;

pub use ui_assembly::UIAssembler;

pub use ui_assembly::UIAssemblyConfig;

pub use ui_assembly::UIComponent;

pub use error::AutomataError;

pub use error::AutomataResult;

pub use traits::Evolvable;

pub use traits::InverseDesignable;

pub use traits::SelfAssembling;

Modules

cayley_navigation

Cayley Graph Navigation for Cellular Automata

error

Error types for automata operations

geometric_ca

Geometric Cellular Automata

inverse_design

Inverse Design for Cellular Automata

self_assembly

Self-Assembly System using Geometric Algebra

traits

Core traits for automata operations

tropical_solver

Tropical Algebra Constraint Solver

ui_assembly

UI-Specific Self-Assembly

Structs

Bivector

Bivector type - wrapper around Multivector with only grade 2

DualMultivector

Multivector with dual number coefficients for automatic differentiation

Multivector

A multivector in a Clifford algebra Cl(P,Q,R)

TropicalMultivector

A geometric algebra multivector in tropical space

Vector

Vector type - wrapper around Multivector with only grade 1