Golden ratio guide

Three looks

Each picture below was drawn by Golden ratio at its opening values. The table under each one is the whole recipe; everything not listed stays as the page opens, and the mode's slider stays at its start.

A seed head

A round seed head of a thousand rainbow dots, larger in the middle, with spiral arms turning both ways — Phyllotaxis with 1000 points, drawn whole.

Each dot sits one golden angle past the one before, a little further out. Because the angle is irrational, no two dots line up, and the eye picks out spiral arms turning both ways.

The dots shrink towards the edge, and their colour turns by the same angle.

Setting	Value
Mode	Phyllotaxis
Auto-animate	Off

Move Points up to 5000 for a denser head, then tap off centre to move it.

A Penrose tiling

A ten-sided Penrose tiling of green and violet triangles, with star shapes spreading from its middle — Penrose tiling split five times, drawn whole.

Ten thin triangles meet in the middle. Each split cuts a thin triangle into two pieces and a thick one into three, always at the golden ratio. Violet pieces are thin, green pieces are thick.

The pieces fill a ten-sided shape with no gaps, yet the pattern never repeats by sliding. See tessellation.

Setting	Value
Mode	Penrose tiling
Auto-animate	Off

Turn Auto-animate back on and press Restart to watch the triangles laid one by one.

Voronoi seeds

The frame filled with muted coloured cells, small in the middle and larger outward, each with a white dot — Voronoi seeds with 80 seeds.

The white dots are placed the same way as the seed head. Each one owns the patch of canvas nearest to it, so the cells grow larger towards the edge and fill the whole frame.

While time runs, the dots turn slowly about the centre and the cells follow them.

Setting	Value
Mode	Voronoi seeds

Press Pause to hold a pattern you like before you save it.