Quilt · Overall
Sierpinski triangle
A triangle divided into four with the middle one left empty, and the same again in each of the three corners: a fractal sewn in fabric.
- Setting
- Overall
- Size
- 60° block, Triangle · 30" × 34⅝"
- Known from
- The mathematics from 1915; quilts from the 1990s
- First known print
- The Polish mathematician Wacław Sierpiński described the triangle in the journal Comptes Rendus in 1915.
- Origin
- Wacław Sierpiński (1915)
- Difficulty
- Medium · Triangles, geese and other angles cut with a ruler
History
The triangle is named after Sierpiński, but the pattern is older than the mathematics: similar triangles in triangles are in the Cosmati mosaics of Italian church floors from the 1200s. It is one of the best-known examples of a fractal, a figure that looks like itself however closely you look.
It is a modern quilt motif, not a traditional pattern. The Science Museum Group in London has "A mathematical quilt" of 1991 by Elaine Krajenke Ellison of Indiana, inspired by Benoit Mandelbrot, and she and Diana Venters published the book Mathematical Quilts in 1999. At the Bridges conference on mathematics and art in 2011, Andreia Hall and Prudência Leite showed the quilt "Sierpinski's Triangle Revisited".
How it is used
In QuiltCrafter it is a 60° block on the triangle lattice: a triangle with four small triangles to a side, the small ones pointing up coloured where Pascal's triangle has an odd number. That gives two steps of the fractal; each new step doubles the side.
The blocks repeat over the whole quilt as triangles in rows, alternately up and down, like Thousand Pyramids.
Related quilts
Sources
The text is our own, written from the sources below. Photos of the old quilts are in the museums' collections.
- Article Wikipedia: Sierpiński triangle
- Museum Science Museum Group: A mathematical quilt, 1991
- Book Diana Venters and Elaine Krajenke Ellison: Mathematical Quilts (1999)
- Article Bridges 2011: Andreia Hall: Sierpinski's Triangle Revisited (2011)