Parametric Gray-Scott Reaction-Diffusion for OpenVCAD

Convert reaction-diffusion mathematics into manufacturable 3D geometry using OpenVCAD's volumetric modeling capabilities.

What This Does

This project transforms Gray-Scott reaction-diffusion equations into 3D printable geometry. Instead of just simulating chemical patterns on screens, we create physical objects where the reaction-diffusion mathematics becomes solid topology.

Key Innovation

• Ready simulation data → 3D manufacturable geometry
• Chemical concentrations → Material distributions
• Pattern evolution → Spatial structures
• Mathematical surfaces → Printable objects

Features

• Parametric control over pattern characteristics
• 3D printing optimized with manifold geometry options
• Direct implementation of Gray-Scott equations from Ready format
• Real-time parameter adjustment for design exploration
• Automatic boundary closure for watertight geometry

Parameters Reference

Primary Controls

threshold - Geometry Amount

• 0.2: Dense, coral-like structures (lots of geometry)
• 0.4: Medium density (balanced)
• 0.6: Sparse, minimal structures (little geometry)

time_param - Pattern Evolution

• 0.0: Early-stage patterns (simple, nucleated)
• 0.5: Mid-evolution (complex interactions)
• 1.0: Mature patterns (fully developed)

frequency_scale - Pattern Size

• 0.5: Large, macro-scale features
• 1.0: Natural scale
• 2.0: Fine, micro-scale details

amplitude - Pattern Intensity

• 0.1: Subtle, gentle patterns
• 0.8: Strong, dramatic patterns

evolution_rate - Spatial Variation

• 0.5: Slow spatial changes
• 2.0: Rapid spatial variation

3D Printing Controls

make_printable (Boolean)

• True: Manifold, watertight geometry with boundary closure
• False: Pure mathematical surfaces (artistic/exploration)

Ready Presets

Try these parameter combinations for different aesthetic results:

"Coral Growth"

threshold = 0.25
time_param = 0.3
frequency_scale = 0.8
amplitude = 0.4

"Crystal Lattice"

threshold = 0.45
time_param = 0.7
frequency_scale = 1.5
amplitude = 0.6

"Organic Maze"

threshold = 0.35
time_param = 0.5
frequency_scale = 1.0
amplitude = 0.4

"Minimal Architecture"

threshold = 0.55
time_param = 0.8
frequency_scale = 2.0
amplitude = 0.3

Example Parameter Sets

Beginner

Simple Coral Structure

threshold = 0.3
time_param = 0.2
frequency_scale = 0.8
amplitude = 0.4
evolution_rate = 1.0
make_printable = True

• Dense, branching coral-like structure; good starting point.

Geometric Lattice

threshold = 0.5
time_param = 0.8
frequency_scale = 1.5
amplitude = 0.5
evolution_rate = 0.8
make_printable = True

• Regular, geometric patterns with solid connectivity.

Advanced

Organic Architecture

threshold = 0.4
time_param = 0.6
frequency_scale = 1.2
amplitude = 0.6
evolution_rate = 1.5
make_printable = True

• Building-like structures with smooth flow; ideal for architectural exploration.

Jewelry Scale

threshold = 0.45
time_param = 0.7
frequency_scale = 2.0
amplitude = 0.3
evolution_rate = 1.8
make_printable = True

• Fine, intricate motifs suited for small prints.

Vase-like Structures

threshold = 0.35
time_param = 0.4
frequency_scale = 0.9
amplitude = 0.5
evolution_rate = 1.2
make_printable = True

• Hollow, vessel-like forms with organic walls.

Artistic Exploration

Abstract Sculpture

threshold = 0.25
time_param = 0.9
frequency_scale = 0.6
amplitude = 0.7
evolution_rate = 2.0
make_printable = False  # visualization only

• Complex, expressive geometry for renderings or experimentation.

Minimal Forms

threshold = 0.6
time_param = 0.3
frequency_scale = 1.8
amplitude = 0.2
evolution_rate = 0.5
make_printable = True

• Clean silhouettes with restrained detailing.

Troubleshooting Cheatsheet

• Too dense: increase threshold (0.4 → 0.5) or decrease amplitude (0.6 → 0.4).
• Too sparse: decrease threshold (0.5 → 0.3) or increase amplitude (0.3 → 0.5).
• Pattern too large: increase frequency_scale (1.0 → 1.5).
• Pattern too small: decrease frequency_scale (1.0 → 0.7).
• Not printable: set make_printable = True

Usage

1. Install OpenVCAD Studio from OpenVCAD releases

2. Load the script:

   • Open VCAD Studio
   • Load gray_scott_parametric.py

3. Adjust parameters:

   • Edit parameter values at the top of the file
   • Reload to see changes

4. Export for 3D printing:

   • Set make_printable = True
   • Export as STL/OBJ from VCAD Studio

Mathematical Background

This implementation converts the Gray-Scott reaction-diffusion system:

∂u/∂t = Du∇²u - uv² + F(1-u)
∂v/∂t = Dv∇²v + uv² - (F+k)v

Into spatial material distributions using trigonometric approximations of the steady-state solutions. The time_param controls which "snapshot" of the temporal evolution becomes the 3D geometry.

Applications

• Biomimetic structures: Tissue scaffolds, bone-like gradients
• Architectural elements: Organic facades, structural optimization
• Art and design: Sculptural objects, jewelry, decorative elements
• Metamaterials: Programmable material properties
• Research: Reaction-diffusion visualization, educational models

Comparison with Traditional Tools

Traditional RD Tools	This Implementation
Screen visualization	Physical 3D objects
Time-domain simulation	Spatial geometry
Single chemical display	Multi-material structures
Research/analysis focus	Manufacturing focus

Requirements

• OpenVCAD Studio (Windows/Mac/Linux)
• 3D Printer (optional, for physical output)
• Slicer software (for 3D printing workflow)

License

This implementation is provided for academic and research use. Please cite appropriately if used in publications.

Contributing

Contributions welcome! Areas for enhancement:

• Additional reaction-diffusion systems (Turing, FitzHugh-Nagumo)
• Parameter optimization algorithms
• Multi-material printing support
• Animation/morphing capabilities

Citations

This work builds upon several key contributions to reaction-diffusion research and simulation:

Ready Simulator

Tim Hutton, Robert Munafo, Andrew Trevorrow, Tom Rokicki, Dan Wills. "Ready, a cross-platform implementation of various reaction-diffusion systems." GitHub: https://github.com/GollyGang/ready arXiv: http://arxiv.org/abs/1501.01990

Gray-Scott System

Pearson, J. E. (1993). "Complex patterns in a simple system." Science, 261(5118), 189-192. DOI: https://www.science.org/doi/10.1126/science.261.5118.189

OpenVCAD Platform

Matter Assembly Computation Lab, University of Colorado Boulder. "OpenVCAD: Systems and Processes for Volumetric Multi-Material 3D Models" GitHub: https://github.com/MacCurdyLab/OpenVCAD-Public

Acknowledgments

• Ready development team for the foundational reaction-diffusion simulation framework
• OpenVCAD development team at University of Colorado Boulder for volumetric modeling capabilities
• Gray-Scott system researchers for the mathematical foundation