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Penrose Tiling Quilt

Here's the original picture that was on this web page:
 
Photographed March 8, 1996 on a snow pile in our back yard.

The pattern is an area selected from a Penrose tiling.
Mark designed the quilt by computer and Serena made it.
This was before Serena knew about "paper piecing".
The 6 colors were chosen to produce a 3-D effect.
The Golden Ratio appears in the relative lengths of the triangle sides.

There are only two kinds of pieces: a 72-36-72 degree triangle and a 36-36-108 degree triangle.

Penrose Tiling:

Several aperiodic tilings discovered by the British mathematician/physicist Roger Penrose.

Tiling:

A way of precisely covering an infinite plane with a fixed set of shapes.

Aperiodic:

Non-repeating. There is no way you can rotate and/or shift the infinite pattern so that the rotated/shifted pattern is the same as the original pattern. (This is not apparent from the quilt because the quilt is not the entire infinite pattern. In fact, we chose a particularly symmetrical part of the infinite pattern.)

Correction/clarification by Dave Green (August 1, 1998):

• The phrase "the infinite pattern" is misleading, since there are an infinite number of different infinite patterns.
• There are two Penrose tilings with five-fold rotational symmetry -- they can be created by radially extending the two implied Penrose tilings in your quilt around a single point (the center of your quilt).

Hanging the Quilt:

The quilt is attached to the hoop with loops of fabric.
For now, they're just pinned on.
Lengths of coat-hanger wire keep the topmost points from flopping.

Related Links:

• Lisbeth G Clemens' Penrose Tiling Quilt
    (If this link doesn't work, wait a week or two and try again.)
• Andrew Krizman's Penrose Tiling Quilt
• Our Polyhedron Quilt
• Jos Leys' Geometry Galleries Very pretty patterns including Penrose tilings.
• Geometry Junkyard (many links).
• Bob - Penrose Tiling Generator and Explorer (Windows ".exe" file)