Fractal pattern generator

Shapes made of smaller copies of themselves, turned into seamless tiles. Choose a Sierpinski carpet or triangle, Koch snowflakes, dragon curves, a Pythagoras tree or another fractal, set the depth, and export the pattern as SVG, PNG or CSS.

Open in the generator How it works

Sierpinski triangles in neon colours on a dark background

What is a fractal?

A fractal is a shape that contains smaller copies of itself, however closely you look. The Sierpinski triangle (Wacław Sierpiński, 1915) is a triangle with a triangular hole whose three corners repeat the same idea; the Koch snowflake (Helge von Koch, 1904) grows smaller triangles on every edge of a triangle.

The Pythagoras tree grows two smaller squares on top of each square (named after the theorem, drawn by Albert Bosman in 1942). The dragon curve, found by NASA physicists in the 1960s, comes from folding a strip of paper again and again.

How the generator builds them

A true fractal has endless detail, so Ornamatic draws it to a chosen depth: each extra step adds a layer of smaller copies. At a finite depth the fractal fits inside one cell, which can then be repeated, so the result is a seamless tile.

Every level can get its own colour, which shows how the shape is built; or switch to one colour, or cut the holes out for a see-through pattern.

What you can adjust

Fractal — Sierpinski carpet and triangle, Vicsek cross, H-tree, Moore curve, Koch snowflakes, dragon curves, an L-system tree or the Pythagoras tree.
Depth — how many steps of detail to draw.
Colouring — a colour per level, a colour per dragon, one colour, or cut-out holes.
Line width — for the fractals drawn with lines.
Colours — any palette.