Penrose — Create Beautiful Diagrams by Typing Math Notation

Introduction

Penrose is a research-driven system from Carnegie Mellon University that turns plain-text mathematical notation into publication-quality diagrams. You describe what you mean in a domain-specific language, and Penrose finds an aesthetically pleasing layout automatically.

What Penrose Does

• Generates 2D diagrams from three plain-text input files (domain, substance, style)
• Uses numerical optimization to find visually appealing element placement
• Supports set theory, linear algebra, geometry, and other mathematical domains
• Exports diagrams as SVG for use in papers and presentations
• Provides a live editor with instant preview for iterative design

Architecture Overview

Penrose separates domain knowledge, concrete instances, and visual style into three files. The compiler parses these into a constraint system, and a numerical optimizer (gradient descent) adjusts element positions and sizes to satisfy all constraints while minimizing an energy function that encodes aesthetic preferences.

Self-Hosting & Configuration

• Install the CLI tool (roger) via npm for local compilation
• Use the web-based editor at penrose.cs.cmu.edu for quick experiments
• Define custom domains by writing .domain, .substance, and .style files
• Style files control colors, shapes, labels, and layout constraints
• Output SVGs can be embedded in LaTeX, HTML, or Markdown documents

Key Features

• Declarative: describe relationships, not coordinates
• Optimization-based layout produces consistent, balanced results
• Extensible domain system for custom mathematical fields
• Interactive editor with real-time diagram preview
• Publication-ready SVG output with proper label rendering

Comparison with Similar Tools

• TikZ/PGF — manual coordinate placement in LaTeX; Penrose auto-layouts
• Mermaid — flowcharts and sequence diagrams; Penrose targets mathematical diagrams
• D2 — general software diagrams; Penrose specializes in math and set theory
• Manim — animated math videos; Penrose produces static publication diagrams
• draw.io — GUI-based drag-and-drop; Penrose is text-first and deterministic

FAQ

Q: Do I need to know programming to use Penrose? A: Basic familiarity with text files helps, but the DSL is designed for mathematicians, not programmers.

Q: Can I use Penrose in LaTeX papers? A: Yes. Export SVGs and include them with standard LaTeX graphics packages.

Q: What mathematical domains are supported out of the box? A: Set theory, linear algebra, graph theory, and geometry ship as built-in domains.

Q: Is Penrose production-ready? A: It is an active research project. The core system works well, though some advanced features are evolving.

Sources

• https://github.com/penrose/penrose
• https://penrose.cs.cmu.edu/