Friday, August 21, 2009

To a new symmetry . . .

I've said it before, but it bears repeating . . .

I've read three books about symmetry and two-dimensional patterns: one written by a mathemetician; the other two written by quilters.

All three books described the four operations of symmetry: translation, rotation, reflection, and glide reflection. All three books generated patterns using a method developed by crystallographers (even though crystallographers are not necessarily quilters, and vice versa). All three books overlooked two simple observations: all the patterns generated could be simplified to two pairs of squares beside each other, on top of each other, or diagonally from each other; and, in all but one instance, the squares were right side up or upside down, but never sideways.

I have previously described the operations of symmetry, but I will not generate any patterns with a method I now view as flawed. I propose a new symmetry which does not rely on any operations other than "pick a pair." I have presented the two tiles below to nearly 300 people. You've had a week or so to play with them.

Will you join me on a guided journey with these tiles??

Thank you for reading . . . please leave a comment and follow this blog. Or, join my Yahoo! group.


  1. still trying to get my "men" into semi-human form...and all their parts the same color. how i wish i had an artist's eye like you!! the ability to "see" a finished project just from the tiles is a talent i lack. i still don't know HOW you were able to see men in these tiles! amazing, simply amazing.

  2. How may I help you?? . . . What colors are you using??

  3. Things I've learned thus far...

    Black, a medium blue and a yellow make good color choices when laying out the tiles, giving light, medium and dark values. Easy to see repeated patterns.

    Stay away from neon-clear, ultra violet and infra red. Those colors clash and they make it hard to see what yor design will actually look like.

  4. You can't go wrong combining light, medium, and dark values in a pattern . . . when the colors all yell, "Look at ME!!" you probably won't . . . use a loud color sparingly, as accent