Monday, July 1, 2013

Math Embroidery: Tessellations

Tessellations are designs created by lining up geometric shapes edge to edge, with no over lapping or gaps.  They are commonly used in tile designs and fabric motifs.  Soccer balls use tessellation to cover a sphere with 2D straight edge polygons.





Six strand cotton on 20 ct linen.  Back stitch.
 Tessellation is used often in quilting design.  Below is a close up of a quilted piece I did using the same motif detailed in the photos both above and below.  I used back stitch, instead of running stitch.
Quilting cotton on cotton fabric.  Back stitch.

Six strand cotton on 20 ct linen.  Back stitch.
Tessellation can be used to solve mathematical problems visually.  For example, Voronoi Tessellation uses data points to create a diagram that shows geographic distance.  The areas shaded represent all the points that are the equidistant from each other.  City planners use Voronoi Tessellation diagrams to determine how far apart shops can be and still impact each other.

Six strand cotton on 20 ct. linen.  Back stitch.
Penrose Tiling is unlike traditional tessellation in that it doesn't have a repeating pattern.  Instead, it relies on reflected symmetry to create a self-similar structure.

Six strand cotton on 20 ct. linen.  Couching, back stitch, chain stitch and split stitch.

Six strand cotton on 20 ct. linen.  Back stitch and chain stitch.