Voronoi Diagram Generator

The Voronoi Diagram Generator partitions a 2D plane into regions based on closeness to a set of seed points. Every point in the plane belongs to whichever seed is nearest, so the diagram looks like a patchwork of cells around the input points. This tool generates Voronoi diagrams interactively in your browser — drop new seeds with a click, drag any seed to redraw the cells in real time, switch between four distance metrics, and apply Lloyd relaxation to even out cell sizes. Export the result as crisp SVG or shareable PNG.

The four distance metrics — visualized

The shape of every Voronoi cell is determined by which distance metric you use. Each metric defines what "a circle" looks like — and that circle's shape is exactly the shape that bumps up against its neighbors to form cell boundaries.

That is why Manhattan-metric cells have only horizontal, vertical, and 45° edges, while Chebyshev cells have only horizontal and vertical edges — the boundary between two cells is always tangent to the shapes of those two "circles". Euclidean gives the classic curved-edged Voronoi everyone associates with the name. Minkowski p=3 is a mathematically elegant in-between case used in computational design where the L1 corners feel too harsh but the L2 circles feel too round.

What makes this generator different

Where Voronoi diagrams show up

• Cell-tower coverage maps — a phone connects to whichever tower it is closest to, which is exactly the Voronoi cell of that tower.
• John Snow's 1854 cholera map — Snow drew the Voronoi cell around each water pump in Soho and counted cholera deaths inside each cell, isolating the contaminated Broad Street pump.
• Procedural texturing — Worley noise (cellular noise) is used in everything from skin shaders to terrain generation in games like Minecraft and No Man's Sky.
• Mesh generation — finite-element solvers prefer near-equilateral triangles, and the Delaunay triangulation (the dual of the Voronoi diagram) maximizes the smallest angle across all triangles.
• Robot path planning — the edges of the Voronoi diagram around obstacle points are the safest paths a robot can take, because they maximize distance from every obstacle.
• Stippling and halftoning — Lloyd-relaxed Voronoi diagrams produce visually pleasing point distributions used in artistic stippling and printer dithering.
• Astronomy — galaxy super-clusters and the cosmic web display Voronoi-like structure thanks to gravitational clumping; Voronoi tessellation is a standard tool in galaxy-density estimation.
• Crystallography — Wigner–Seitz cells (Voronoi cells around atoms in a lattice) define the primitive volume of every unit cell in solid-state physics.

Mathematical detail

How to use this tool

1. Pick a preset or set up the form. The preset chips at the top of the form are one-click starting points — Classic Cells, Honeycomb, City Blocks, Chess King, Golden Spiral, Ripples, Lloyd Relaxed, Wireframe, Stipple Ink, 3 Territories.
2. Choose the distance metric. Euclidean for the classic look, Manhattan for blocky cells, Chebyshev for axis-aligned squares, Minkowski p=3 for rounded-square in-between cells.
3. Click Generate. The diagram renders with an animated cell-growth reveal so you see how each seed "claims" its territory.
4. Edit on the canvas. Click empty space to add a new seed point. Drag any seed dot to move it — the cells follow your finger in real time. Double-click a seed to delete it.
5. Polish with Lloyd relaxation. Click the Lloyd relax button (or press R) to nudge every seed toward its cell's centroid. A few passes give you a visually uniform tessellation.
6. Switch metric without losing your point set. Use the metric pills above the canvas — the same seeds, different distance rule, dramatically different cells.
7. Export. SVG for vector use, PNG for raster sharing, or copy PNG straight to clipboard.

Tips for getting great-looking diagrams

• For visually uniform cells, start with a Random or Uniform layout and apply 3–4 passes of Lloyd relaxation. You will see the cells converge toward a hexagonal pattern with very similar sizes.
• For pop-art posters, use the Cluster layout with the Rainbow palette and turn on cell edges. The three territories produce a striking visual hierarchy with bold color blocks.
• For technical-looking diagrams, use the Wireframe style on a Uniform layout — the clean black lines on white background read like a CAD drawing.
• For organic, hand-drawn patterns, use the Stipple style — the algorithm reads cell edges as dotwork and produces a pen-and-ink look used in scientific illustration.
• For mathematical clarity, switch to Manhattan or Chebyshev with a small point count (8–12 points). The right-angle edges make it easy to trace by hand why each cell has the shape it does.

Frequently asked questions