Model Library
このページでは、現在システムに登録されている全てのL-Systemモデルを表示します。 各モデルには、その数理的特徴とプレビュー画像が自動的に付与されています。
LSystems.FibonacciFractal — Type
FibonacciFractal{N, T} <: AbstractTiles{N, T}Fibonacci Fractal L-system configuration. Generates a sequence of line segments whose lengths correspond to Fibonacci numbers.
Visual Representation
Configuration
| Property | Value |
|---|---|
| Axiom | S |
| Angle | 90° |
| Accept Symbols | ["L", "S"] |
Metadata
| Key | Value |
|---|---|
| Source File | fibonacci.json |
| Type | L-System |
LSystems.GosperCurve — Type
GosperCurve{N, T} <: AbstractTiles{N, T}A hexagonal space-filling curve that tiles the plane with 'Gosper islands'. It maps hexagonal/triangular lattices to a 1D chain, making it uniquely suited for studying quantum systems with C6 symmetry (like graphene) using 1D tensor network methods like DMRG.
Visual Representation
Configuration
| Property | Value |
|---|---|
| Axiom | A |
| Angle | 60° |
| Accept Symbols | ["A", "B"] |
Metadata
| Key | Value |
|---|---|
| Source File | gospercurve.json |
| Type | L-System |
LSystems.HeighwayDragon — Type
HeighwayDragon{N, T} <: AbstractTiles{N, T}A fractal curve generated by a recursive folding process. While not a simple grid-filler, its boundary and internal structure exhibit complex self-similarity. It is often studied in the context of fractal growth models and non-trivial tiling of the complex plane.
Visual Representation
Configuration
| Property | Value |
|---|---|
| Axiom | FX |
| Angle | 90° |
| Accept Symbols | ["F"] |
Metadata
| Key | Value |
|---|---|
| Source File | heighwaydragon.json |
| Type | L-System |
LSystems.HilbeltPath — Type
HilbeltPath{N, T} <: AbstractTiles{N, T}Standard space-filling curve tiling a square grid. By recursively mapping 2D coordinates to a 1D sequence, it preserves spatial locality more effectively than simple raster scanning. This makes it a cornerstone for designing 1D paths in Matrix Product State (MPS) simulations of 2D quantum systems.
Visual Representation
Configuration
| Property | Value |
|---|---|
| Axiom | A |
| Angle | 90° |
| Accept Symbols | ["F"] |
Metadata
| Key | Value |
|---|---|
| Source File | hilbeltpath.json |
| Type | L-System |
LSystems.KochCurve — Type
KochCurve{N, T} <: AbstractTiles{N, T}A fundamental fractal curve defined by an iterative subdivision of a line segment. It demonstrates the concept of infinite length within a bounded space. In physical contexts, it serves as a model for studying wave scattering and boundary effects in fractal-shaped conductors or resonators.
Visual Representation
Configuration
| Property | Value |
|---|---|
| Axiom | F |
| Angle | 60° |
| Accept Symbols | ["F"] |
Metadata
| Key | Value |
|---|---|
| Source File | kochcurve.json |
| Type | L-System |
LSystems.KochSnowflake — Type
KochSnowflake{N, T} <: AbstractTiles{N, T}The closed-loop form of the Koch curve starting from an equilateral triangle. It is a classic example of a shape with a finite area but an infinite perimeter. Used in condensed matter physics to model fractal interfaces, heat transfer in complex boundaries, and the distribution of vibrational modes on fractal membranes.
Visual Representation
Configuration
| Property | Value |
|---|---|
| Axiom | F++F++F |
| Angle | 60° |
| Accept Symbols | ["F"] |
Metadata
| Key | Value |
|---|---|
| Source File | kocksnowflake.json |
| Type | L-System |
LSystems.PeanoPath — Type
PeanoPath{N, T} <: AbstractTiles{N, T}The first discovered space-filling curve (1890). It tiles a square lattice using a 3x3 recursive decomposition. In the context of lattice models, it provides an alternative 1D traversal path for 2D systems, offering different locality properties compared to the 2x2 based Hilbert curve.
Visual Representation
Configuration
| Property | Value |
|---|---|
| Axiom | X |
| Angle | 90° |
| Accept Symbols | ["F"] |
Metadata
| Key | Value |
|---|---|
| Source File | peanocurve.json |
| Type | L-System |
LSystems.PenroseLSystem — Type
PenroseLSystem{N, T} <: AbstractTiles{N, T}An L-system implementation of the P3 Penrose tiling, exhibiting five-fold rotational symmetry and non-periodic order. This model is essential for exploring electronic states and topological phases in quasicrystals, where traditional Bloch theorem and periodic boundary conditions are no longer applicable.
Visual Representation
Configuration
| Property | Value |
|---|---|
| Axiom | [X]++[X]++[X]++[X]++[X] |
| Angle | 36° |
| Accept Symbols | ["F"] |
Metadata
| Key | Value |
|---|---|
| Source File | penrose.json |
| Type | L-System |
LSystems.SierpinskiGasket — Type
SierpinskiGasket{N, T} <: AbstractTiles{N, T}A recursive fractal based on triangular subdivision, resulting in a lattice with a Hausdorff dimension of approximately 1.585. It is widely used to study quantum transport, percolation, and spectral densities in systems where Euclidean connectivity is broken, providing insight into how dimensionality affects physical phase transitions.
Visual Representation
Configuration
| Property | Value |
|---|---|
| Axiom | A |
| Angle | 60° |
| Accept Symbols | ["A", "B"] |
Metadata
| Key | Value |
|---|---|
| Source File | sierpinskigasket.json |
| Type | L-System |