Free Printable Sierpinski Fractals
Print Sierpinski fractals to color: shapes cut again and again into smaller copies of themselves, so that the same pattern appears at every scale. The triangle keeps three half-size copies of itself at each step, the carpet eight smaller squares, the pentagon five pentagons and the hexagon six hexagons.
Each shape has its own set: an outline at every step, from the first cut to the finest one that still leaves room to color, one page that lines up the early stages, and one that numbers each hole after the cut that made it, with a color key. The sheets are drawn from exact geometry and print sharp at any size.
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Last updated on Tue, 03 Nov 2026 00:31:20 GMT
About the Sierpinski fractals
What a fractal is
A fractal is a shape made of smaller copies of itself. Start with a full triangle, cut out its middle, and three triangles remain; cut the middle out of each of those, and nine remain. Repeated forever, the cuts give a figure that looks the same however closely you zoom in.
Four shapes, one idea
Wacław Sierpiński, a mathematician from Poland, presented the triangle in 1915 and the carpet, a square cut into nine with the center removed, in 1916. The pentagon and the hexagon follow the same rule with five and six copies, and the hexagon hides the outline of a Koch snowflake in its center.
Three kinds of sheets
An outline at a single step is a coloring page, simple at step 1 and intricate at the finest steps. The steps sheet shows steps 0 to 3 together, to watch the pattern grow. On a color by step page, each hole bears the number of the step that cut it, and a key at the bottom lets the child choose one color per number.
Math in the coloring
Counting the pieces gives powers: the triangle has 3, 9, then 27 pieces, the carpet 8, 64, then 512. The colored area shrinks at each step while the number of pieces grows, the paradox at the heart of every fractal.
