01

Begin with the question

Delaunay Triangulation, Made Visual starts with one useful question: The companion structure that connects nearby points without skinny surprises.

Delaunay triangles connect nearby points while avoiding points inside each triangle’s circumcircle. The point is not to memorize a label. It is to notice a repeatable relationship, then test what changes when one part of that relationship moves. Instructions become images when you give a rule room to repeat.

02

Build a working model

The main diagram is a point cloud toggling from dots to clean triangulation. It gives the eye a before-and-after view rather than asking it to infer the rule from a paragraph alone.

A working model can be simple and still be powerful: name the parts, hold one choice steady, change another, and compare the result. That is how this topic becomes something you can inspect instead of only admire.

THE LITTLE FORMULArule + seed + iteration → variation
  • Name the part that repeats.
  • Choose one change to test.
  • Compare the new result with the first one.
03

Try a small experiment

Flip one diagonal in a four-point shape and compare the triangles. Open Start a sketch when it fits the question, and keep a note of the setting, rule, or observation that changes the picture most clearly.

If this guide does not need a generator, recreate the diagram on paper: trace the underlying structure first, then add the decorative detail. The structure should still read before the decoration arrives.

  • Start with: Point cloud toggling from dots to clean triangulation.
  • Make two variations, changing only one choice each time.
  • Keep the version that teaches you the most, not only the prettiest one.
04

What to notice next

Voronoi and Delaunay diagrams are dual views of the same point set. Return to Delaunay Triangulation, Made Visual in a photograph, a built object, or another artwork. Ask where the model fits and where it does not.

That habit—observe, model, test, and revise—connects this lesson to every other guide in the Generative Systems collection.

NOW MAKE IT MOVE

Turn the idea into an experiment.

The quickest way to understand a pattern is to change it and watch what happens.

Start a sketch