Golden ratio guide

Overview

Golden ratio draws the shapes that grow out of one number, about 1.618.

A golden spiral of coloured quarter-circle arcs running through nested squares on a dark grid
The Fibonacci spiral at depth 12, drawn whole with Auto-animate off.

The golden ratio, written phi, is the proportion where the whole is to the long part as the long part is to the short. It is an irrational number.

Five modes draw what follows from it: a Fibonacci spiral of quarter-circle arcs, a phyllotaxis seed head, a Penrose tiling, Voronoi seeds and a golden rectangle cut down square by square.

Load a photo and the same proportions become a composition grid over it: a golden spiral, the rule of thirds, a phi grid or a golden triangle.

You can save the canvas as a PNG or copy it.

Open Golden ratio Start here

In this guide

  1. StartWhat you need, your first spiral, and saving it.
  2. Every controlEvery mode and control, one line each.
  3. Three looksThree pictures and the settings that made them.
  4. HelpWhat to do when something goes wrong.

It runs in your browser on a 2D canvas. It needs no GPU and nothing is uploaded. A mouse, a trackpad, a pen and a finger all work.