Peano Curve Generator

What is a Peano Curve?

A Peano curve is a space-filling curve, which means it's a continuous curve that passes through every point in a square. It was discovered by Giuseppe Peano in 1890, making it the first known space-filling curve in mathematics.

How Peano Curves Work

The Peano curve is constructed recursively. At each iteration:

1. The square is divided into a 3×3 grid (9 smaller squares)
2. Each small square is visited in a specific pattern
3. The pattern alternates between normal and reflected orientations
4. The process repeats for each small square

Mathematical Properties

• Dimension: The Peano curve has a Hausdorff dimension of 2
• Continuity: It's a continuous, surjective function from [0,1] to [0,1]²
• Self-similarity: Each section is a scaled copy of the whole curve
• Nowhere differentiable: The curve has no tangent at any point

Common Use Cases

• Computer Graphics: Texture mapping and image processing
• Mathematics Education: Teaching fractal geometry and limits
• Data Structures: Spatial indexing and database queries
• Art & Design: Creating intricate fractal patterns
• Signal Processing: Multi-dimensional data traversal

Related Curves

• Hilbert Curve: Another space-filling curve with 2×2 subdivisions
• Sierpiński Curve: Based on the Sierpiński triangle
• Moore Curve: A closed version of the Hilbert curve

Privacy & Security

All curve generation happens locally in your browser using JavaScript and HTML5 Canvas. Your data never leaves your device - complete privacy guaranteed.