L-System Explorer

A real-time 3D L-system visualization tool built with Bevy. Explore parametric grammars with PBR materials, physics-based tropism, genetic breeding, and batch export — in the browser or on desktop.

Try it in the browser

Features

Grammar Engine

• Parametric Rules — Define production rules with parameters, conditions, and stochastic probabilities
• Context-Sensitive Matching — Left/right context operators with #ignore for skipping turtle symbols
• Two-Pass Derivation — Separate growth and finalization (decomposition) phases for cleaner grammar design
• Async Derivation — Background thread compilation prevents UI freezing during high-iteration generation

Rendering

• Real-time Editing — Live grammar compilation with debounced auto-update
• Parallel Transport Framing — Smooth branch geometry without gimbal lock
• 3 PBR Material Slots — Base color, emission, roughness, metallic, UV scale, and procedural textures per slot
• Prop System — Spawn discrete meshes (leaf, sphere, cone, cylinder, cube) at grammar-defined positions
• Tropism & Elasticity — Gravity-influenced growth simulation

Genetic Breeding (Nursery)

• Interactive Evolutionary Computation — 3x3 population grid rendered in 3D world space
• Champion Selection — Click individuals to mark as breeding parents; selected plants show translucent highlight panels
• Mutation & Crossover — Evolve rules, constants, materials, angles, step sizes, widths, elasticity, and tropism
• Adjustable Mutation Rate — Control evolution intensity per generation
• Preset Injection — Load any preset into selected champions as a starting point
• Error Visualization — Failed derivations shown with red panels and error messages

Export

• OBJ — Wavefront format with per-mesh material references
• GLB — Binary glTF 2.0 with full PBR materials
• Batch Variations — Generate multiple stochastic variants in one operation with async progress tracking

Platform

• Native — Desktop app with full performance
• WASM — Runs in the browser via WebAssembly

Quick Start

# Native
cargo run --release

# WASM
rustup target add wasm32-unknown-unknown
cargo build --target wasm32-unknown-unknown --release

Built-in Presets

Presets from Prusinkiewicz & Lindenmayer's The Algorithmic Beauty of Plants:

Preset	ABOP Reference	Highlights
Quadratic Koch Island	Fig 1.6	Fractal space-filling curve
Sierpinski Gasket	Fig 1.10b	Two-pass decomposition example
Branching Pattern	Fig 1.39	Parametric binary tree with tapering
Monopodial Tree	Fig 2.6	Spiral phyllotaxis, 3 branch types
Sympodial Tree	Fig 2.7	Sympodial branching architecture
Ternary Tree (Gravity)	Fig 2.8	Tropism and elasticity simulation
Ternary Tree (+Props +Materials)	—	Stochastic rules, 3 materials, leaf and sphere props

Grammar Syntax

Directives

Directive	Description
#define NAME VALUE	Define a constant for use in rules
#ignore: SYMBOLS	Skip symbols during context matching
omega: ...	Set the axiom (starting state)
pN: PRED : COND -> SUCC	Production rule with optional condition

Turtle Commands

Symbol	Parameters	Description
F	(length)	Move forward, drawing a branch segment
f	(length)	Move forward without drawing
+	(angle)	Turn left (yaw)
-	(angle)	Turn right (yaw)
&	(angle)	Pitch down
^	(angle)	Pitch up
/	(angle)	Roll clockwise
\	(angle)	Roll counter-clockwise
|		Turn around (180 degrees)
$		Roll to vertical (align up with world Y)
[		Push state onto stack
]		Pop state from stack
!	(width)	Set branch width

Material & Prop Commands

Symbol	Parameters	Description
,	(id)	Switch to material ID (0, 1, or 2)
'	(r, g, b)	Set vertex color (0.0–1.0 per channel)
~	(prop_id, scale)	Spawn a prop at current position

Prop ID to mesh mapping (configurable in the UI):

• 0 = Leaf, 1 = Sphere, 2 = Cone, 3 = Cylinder, 4 = Cube

Conditions

Condition	Description
*	Always match (wildcard)
PROB	Stochastic: match with probability (0.0–1.0)
x > N	Parameter comparison
x = N	Parameter equality

Context-Sensitive Rules

LEFT_CONTEXT < PREDECESSOR > RIGHT_CONTEXT : CONDITION -> SUCCESSORS

• Left context (<): Symbols that must appear immediately before the predecessor.
• Right context (>): Symbols that must appear immediately after the predecessor.
• Either or both contexts can be omitted for context-free rules.

Use #ignore to skip turtle commands during context checks:

#ignore: + - & ^ / \ [ ]

Signal propagation example (acropetal flow):

#ignore: + - & ^ / \ F
omega: B(1) A A A A
p1: B(x) < A -> B(x+1)
p2: B(x) -> B(x)

After 1 iteration: B(1) B(2) A A A — the signal B propagates rightward.

Two-Pass Derivation (Finalization)

Separate growth from decomposition (ABOP Chapter 1.3):

1. Growth Phase — Main grammar rules execute for N iterations, producing abstract symbols.
2. Finalization Phase — A second rule set runs once, decomposing abstract symbols into concrete turtle commands.

In the UI, expand the Finalization (Decomposition) panel below the grammar editor. Constants from the growth phase carry over.

For presets, use the /// DECOMPOSITION /// separator:

#define n 5
omega: A(n)
p1: A(x) : x > 0 -> F I(x) [ + A(x-1) ] [ - A(x-1) ]
p2: I(x) -> I(x)
/// DECOMPOSITION ///
p1: I(x) -> F(x*2)

Example Grammars

Simple Binary Tree

omega: A
p1: A -> F [ + A ] [ - A ]

Parametric Tree with Tapering

#define wr 0.707
omega: A(100, 10)
p1: A(l, w) -> !(w) F(l) [ &(30) A(l*0.7, w*wr) ] A(l*0.9, w*wr)

PBR Multi-Material Tree

#define MAX 5
omega: ,(0) '(0.5, 0.3, 0.2) A(MAX)
p1: A(t) : t > 0 -> !(t*0.1) F(10) [ &(35) ,(1) '(0.2, 0.8, 0.2) B(t-1) ] A(t-1)
p2: B(t) : t > 0 -> F(5) ~(0, 0.5)

Stochastic Branching

omega: A(50)
p1: A(s) : 0.5 -> F(s) [ + A(s*0.7) ] [ - A(s*0.7) ]
p2: A(s) : 0.5 -> F(s) [ & A(s*0.7) ]

Camera Controls

• Middle Mouse + Drag — Pan
• Right Mouse + Drag — Orbit
• Scroll Wheel — Zoom

Architecture

Split Reactivity

The update loop distinguishes between two independent dirty paths:

• Geometry Dirty — Triggered by grammar, iteration, or interpretation changes. Runs async derivation on a background thread, then rebuilds the mesh.
• Material Dirty — Triggered by palette edits (color, roughness, metallic, UV scale, texture). Only updates shader parameters — no geometry rebuild.

Tweaking material colors never causes expensive tree regeneration.

Building

Requirements

• Rust 1.85+ (Edition 2024)
• For WASM: wasm32-unknown-unknown target

Native

cargo build --release
cargo run --release

WASM

rustup target add wasm32-unknown-unknown
cargo build --target wasm32-unknown-unknown --release

Tests

cargo test

Dependencies

• Bevy 0.18 — Game engine and renderer
• bevy_egui — Immediate mode UI
• bevy_panorbit_camera — Orbit camera controls

Symbios Ecosystem

L-System Explorer is the reference application for the Symbios crate family:

• symbios — L-system parsing and derivation engine
• symbios-turtle-3d — 3D turtle interpreter
• symbios-genetics — Genetic operators for evolution
• bevy_symbios — Bevy integration: mesh generation, PBR materials, and export

References

• Prusinkiewicz & Lindenmayer, The Algorithmic Beauty of Plants (ABOP)
• L-system — Wikipedia

License

Apache License 2.0