I trust you've been playing with your set of design tiles . . . If you don't have a set of design tiles, I suggest you leave your name and email addy here, and I'll send you a set.
Have you been keeping a block log?? With thousands of 4-patch blocks and millions of 9-patch blocks, just how good is your memory anyway?? . . . Merely use the numbers in the upper left (or right) corners, separated by hyphens.
You're gonna have to have your tiles handy, because I'm gonna describe some things in this post, and I want you to SEE for yourself, rather than me just showing you . . .
4-Patch Blocks and Patterns
Lay out four tiles of your choosing . . . as an example, I'm using 1-1-1-2:
Now, lay out three more identical 4-patch blocks:
Do you see the emerging pattern?? Now, move the left column to the right side of the pattern:
Now, instead of four 4-patch blocks of 1-1-1-2, I have four 4-patch blocks of 1-1-2-1. The pattern remains the same, only "shifted" to the left. Now, move the top row to the bottom of the pattern:
Now, instead of four 4-patch blocks of 1-1-2-1, I have four 4-patch blocks of 2-1-1-1. Again, the pattern remains the same, only "shifted" upwards. I could continue moving columns and rows of tiles, "shifting" the pattern as I do.
So, although 1-1-1-2, 1-1-2-1, 1-2-1-1, and 2-1-1-1 describe four distinct 4-patch blocks, the pattern remains the same for all of them. This should be the same for the four 4-patch blocks you're working with.
9-Patch Blocks and Patterns
When I was studying the symmetries I found in other books, I could easily reduce them to a 4-patch block. Repeating the 4-patch block generated the pattern. The same does not hold true for 9-patch blocks.
Using the four 2-1-1-1 blocks above, I can form four different 9-patch blocks. These blocks generate four different patterns. Group your tiles as shown below . . . if you have enough copies of tiles, lay out three identical 9-patch blocks:
By their very nature, 9-patch blocks are "odd." Though they connect with each other, they do not "shift" the pattern repeat as they do with 4-patch blocks. There are a few arrangements that are more or less symmetrical. One arrangement alternates two tiles, checkerboard fashion; one arrangement uses one tile to form a cross in the center of the block, with a different tile in the four corners; and, one arrangement uses diagonal groupings of three tiles.
As always, thank you for reading this post. Please feel free to leave a question or comment, and follow this blog.