Penrose pattern #5, 17/7/11: The Stars Draw Near

Title: The Stars Draw Near
Date: 17 July 2011
Type: Pattern
Number of tiles: 330
Color breakdown: 175 yellow, 165 blue
Shape breakdown: 210 kites, 120 darts
Kosher Penrose tiling rules: no

Penrose pattern #4, 10/7/11: The Hive Mind

Title: The Hive Mind
Date: 10 July 2011
Type: Pattern
Number of tiles: 192
Color breakdown: 52 purple, 88 yellow, 52 blue
Shape breakdown: 116 kites, 76 darts
Kosher Penrose tiling rules: no

Penrose patterns #3a, 3/7/11: The Bright Kaleidoscope

Title: The Bright Kaleidoscope
Date: 3 July 2011
Type: Pattern
Number of tiles: 295
Color breakdown: 135 purple, 145 yellow, 115 blue
Shape breakdown: 230 kites, 165 darts
Kosher Penrose tiling rules: no

I can't change the color of the Penrose tiles, but I can mess with the colors in iPhoto. This one messed with exposure, sharpness, contrast and temperature. The shape is six asters of a larger size (mama kites and some darts added in), with five partial asters filling in the gaps.

Some of this stuff is starting to look like cool logos to me.

Penrose patterns #2a and 2b, 3/7/11: The Aster Fields

Title: Aster Field #1
Date: 3 July 2011
Type: Pattern
Number of tiles: 290
Color breakdown: 100 blue, 90 yellow, 90 blue
Shape breakdown: all kites
Kosher Penrose tiling rules: no

Title: Aster Field #2
Date: 3 July 2011
Type: Pattern
Number of tiles: 375
Color breakdown: 135 blue, 120 yellow, 120 blue
Shape breakdown: all kites
Kosher Penrose tiling rules: no
Supplier: SeriousPuzzles.com

I'm going to be doing more work with the aster pattern, the rounded shape made from 15 kites with the star shaped gap in the middle. If five darts were added, it would be a star with a star shaped gap in the middle, but by rounding the shape, the outside corners fit exactly into the dents and allow for infinite replication, though it does not count as a tesselation because of the arrow shaped gaps.

The new toys have arrived, part 1.

Yay, I have my new toys!


Have you ever wondered what 648 Penrose tiles look like in a big clump on a table?

Wonder no longer.


Here are all the yellow tiles in neater piles. Each color has 132 kites and 84 darts. The rules of Penrose tilings make the bigger pieces more useful.


And then I put each color and shape in its own container because I'm anal.

(As Diane Keaton said in Annie Hall, "Anal is the nice word for what you are.")

In any case, I want to give a shout out to SeriousPuzzles.com, the online store where I was able to get all these cool toys. If looking at the odd things I create gives you the itch to have a set of tiles or two or six, drop them a line.

Penrose pattern #1, 27/6/11: The Violet

Title: The Violet
Date: 27 June 2011
Type: Pattern
Number of tiles: 300
Color breakdown: 165 purple, 75 yellow, 60 blue
Shape breakdown: 195 kites, 105 darts
Kosher Penrose tiling rules: no
Supplier: SeriousPuzzles.com

Notes: Penrose patterns mean I want to make a finite shape that may or may not include gaps. This one has little white triangle gaps and a central pentagonal gap.

There will also be Penrose tilings, which means patterns without gaps that when repeated will fill an entire plane.

Rules of Kosher (or Halal, no prejudice): Gaps are not allowed in Kosher. Rhombi, where a dart and kite meet to form a parallelogram, are the other unacceptable pattern in Halal.

You might see faces in these patterns rather than a five fold symmetrical flower. That's called pareodolia, the name for the human tendency to see faces in even completely random patterns. It was a valuable evolutionary tool waaaaaay back in the day, and it's still part of our standard mental skill set.

This gives you an idea of the size and what it looked like in the room.

Changing the focus and light intensity in iPhoto gives you an idea of the geometry in my head when I designed this.

Get used to these. Or not.

Either way, there's going to be a lot more of them.

I'd be glad to know what you think of them, positive or negative.

Penrose sketches, 19.6.11: Five fold symmetry in nature and with tiles.

Five fold symmetry appears in many shapes in nature. The most famous is probably the starfish, but many flowers like the one pictured above have a pattern that starts at a central point and radiates out just about equally in five directions, each one a 72 degree turn away from its nearest neighbor.

Here is a simple Penrose tile pattern with five fold symmetry that resembles a five fold symmetry flower. I used fifteen yellow kites and topped of that central pattern with ten blue darts just to highlight the yellow more, since the pattern is currently fixed to my off-white refrigerator. Right now, I am experimenting with this fifteen kite pattern to see what can be made with it. Recall that we can make larger shapes similar to the kite using Penrose tiles.

This is my favorite design using fifteen kites. Depending on my mood, I see a gear in a machine or a modern logo. More whimsically, I see a hitchhiking cartoon bird whose head, feet, tail feathers and hitchhiking fist with thumb are all the same size.

Here is a sketch for a larger work using the fifteen kite shape, this time with fifteen Daddy Kites, each made of five kites and three darts. My first idea was to make the outside of the pattern all purple, but with my 216 tiles, it was not possible.

I call this a sketch because some time this week, I should be getting another 432 tiles from SeriousPuzzles.com, as well as some other toys I will be playing with. Then I will be able to make the final version of my original concept using Grandaddy Kites, which should be made of thirteen kites and eight darts, but instead are composed of twelve kites, seven darts and a gap the shape of a large dart, which is not possible to make, as proven here last week.

I'll be giving SeriousPuzzles.com some link love on all my Penrose tiling posts, and they will be using some pictures of my shapes and patterns on their website.

Mutual backscratching aside, I've been very happy with the customer service from them, whether things were immediately in stock or on back order. My thanks to Chris Dillon and all the rest of the staff.

Penrose sketches, 16.6.11: Five fold symmetry with three kites.

Here are three kites put together. If there were five kites centered around the angle at the bottom, it would create a regular decagon, a ten sided polygon. The angle for the gap at the bottom is 144°, which is an angle that can be filled many ways. The idea is to take five of these three kite shapes, twist them by the same angle each time to make the patterns below. The first is using the regular kite shape and a two color pattern, the second is using the larger kite I call the Mama Kite, again using just two colors, and the last is using the Papa Kite and three colors.

Completed: 15 June 2011
15 tiles, all kites
5 yellow, 10 purple

Completed: 16 June 2011
45 tiles
30 kites and 15 darts
20 yellow and 25 blue

Completed: 16 June 2011
120 tiles
75 kites and 45 darts
40 yellow 40 purple and 40 blue