Sunday, June 5, 2011

Still playing with the new toys.

I'm still in that lovely honeymoon period with my new toys, the Penrose tiles I bought online at seriouspuzzles.com. With tiles, the "usual" idea is to fill up the plane with patterns, possibly repeating and possibly not repeating. If I put a kite and a dart together like above, I make a rhombus. It's easy to tile the plane with any rhombus in a repeating pattern, and even the non-repeating patterns using rhombi are usually simple variations on a theme.

One way to break away from the rhombus is to make this shape with a dart and two kites, which is really a bigger kite. I started making patterns with this as my main basic shape.

In this first tiling, I started with the nearly round shape in the middle (actually a decagon, a ten sided polygon), and started building out from it using the new big kite shape and the "bow tie", which is a two big kites that share a small kite.

Here I was trying to see what tiles would have to be used if I surrounded one decagon with five other decagons that have a bow tie buffer between them. As you might be able to see, I had to use some rhombi as buffers between the new decagons.

Messing around with even this size of puzzle makes me wonder if I need to buy one more container of tiles.

If anyone knows the name of a local Penrose Tile addiction support group, please send it to me discreetly.

I also did something much simpler on an unusual tack. Instead of trying to tile the plane, I started looking at simple shapes that could be made with relatively few tiles that would use negative space. Here five darts are put together to make a negative space regular pentagon with a pointy star created in purple.

Trying to think of star shapes that have a hole in the center, I thought this kind of looked like a ninja throwing star, known as a shuriken.

I call this the Thin Penrose Shuriken.

This is to distinguish it from a similar idea using the kites instead of the darts, which is the Thick Penrose Shuriken.

With kites, there is a second Thick Penrose Shuriken. To me, this looks more like a rotating gear, so I'm also calling it a Regular Penrose Cam.

This is to distinguish it from a mix and match use of kites, the Irregular Penrose Cam.

I Googled "penrose tiles negative space", but I didn't find anything looking like these last four patterns anywhere on the net. I may have stumbled on a new idea.