QuasiCrystal.jl

In this module, QuasiCrystals structures are available including,

• Fibonacci Lattice
• Penrose Tile
• Amman Beenker Lattice

Package quality is checked on CI via Aqua.jl (Aqua.test_all), covering ambiguities, unbound type parameters, undefined exports, stale dependencies, and Method-of-piracy.

Features

Unified AbstractLattice Interface

QuasiCrystal.jl provides a unified interface (AbstractLattice{D}) that allows both periodic lattices and aperiodic quasicrystals to be accessed consistently. This design enables applications like Lattice2DMonteCarlo to work uniformly with either structure type through consistent access to:

• Sites/positions: Access vertex positions in the structure
• Bonds/connections: Query nearest-neighbor relationships
• Indexing: Uniform site and bond indexing

Key Types

• AbstractLattice{D}: Base abstract type for all lattice-like structures in D dimensions
• AbstractQuasicrystal{D}: Abstract type for quasicrystals (inherits from AbstractLattice)
• AbstractTopology{D}: Abstract type for periodic lattice topologies
• UnitCell{D,T}: Unit cell definition for periodic lattices
• Lattice{Topology,T,B,I}: Concrete type for periodic lattices with unit cell structure
• QuasicrystalData{D,T,TileType}: Data structure for generated quasicrystal patterns
• Bond: Represents connections between sites
• Connection: Connection rules for unit cell-based lattices

Common Interface Methods

# Works for both quasicrystals and periodic lattices
get_positions(lattice)           # Get site positions
get_bonds(lattice)               # Get bond list
get_nearest_neighbors(lattice)   # Get neighbor indices for each site
num_sites(lattice)               # Total number of sites
num_bonds(lattice)               # Total number of bonds

# Build nearest-neighbor connectivity
build_nearest_neighbor_bonds!(qc_data; cutoff=2.0)

Example

Quasicrystal Generation and Analysis

using QuasiCrystal

# Generate a Fibonacci lattice (1D quasicrystal)
fibonacci_qc = generate_fibonacci_projection(20)

# Build nearest neighbor bonds
build_nearest_neighbor_bonds!(fibonacci_qc; cutoff=2.0)

# Access properties via unified interface
println("Number of sites: ", num_sites(fibonacci_qc))
println("Number of bonds: ", num_bonds(fibonacci_qc))

positions = get_positions(fibonacci_qc)
bonds = get_bonds(fibonacci_qc)
neighbors = get_nearest_neighbors(fibonacci_qc)

# Generate a 2D Penrose tiling
penrose_qc = generate_penrose_projection(3.0)
build_nearest_neighbor_bonds!(penrose_qc; cutoff=1.5)

Periodic Lattice Unit Cells

# Get unit cell for square lattice
uc = get_unit_cell(Square)

# Access unit cell properties
println("Basis vectors: ", uc.basis)
println("Sublattice positions: ", uc.sublattice_positions)
println("Connections: ", uc.connections)

See example/lattice_interface.jl for a comprehensive demonstration of the unified interface.

Additional Examples

Tight-binding model is available in example/tight_binding.jl