Listing band scale #5

the question

Is there a shape, which when repeated, can create a Mobius strip?

Yep, there is. Really all you have to do is chop up a strip into squares, however many pieces you want and there you go, done. That was easy. Maybe I’m not asking the right question.

the better question

Is there an asymmetrical shape which interlocks with itself to create a continuous band on a non-orientable surface?

That one is a lot better, but it seems a little unrealistic that I would have started out wondering that instead of the first question.

an answer

To create a simple shape that tiles rectilinearly, you can start with a square, and any change you make to one side, you make the opposite change to the other side. So, if you squish in from the right, you squish out from the left. Continue until you have something interesting.

diagram of individual scale

Listing bands have the additional twist (pun intended) that at some point, the top of one tile (or “scale” which is what I’m calling the individual components) is eventually going to have to fit in with the reverse of the bottom of another. Only bands made up of odd numbers of scales will work. This is probably easiest to understand if you consider that just one scale, twisted into a band would have to fit into itself this way, and one is an odd number. Even numbers simply twist too many times for an asymmetrical scale.

This particular band is made up of nineteen scales, shown above. They were fabricated from .03″ mild steel and allowed to rust naturally. The scales were designed so that just the right amount of twist and bend could happen with this size and material.

wire used to links scales together

The base was constructed from fir and walnut. Displaying a band this large was a challenge, since it sort of collapses if it’s set on the floor. The base allows easy viewing from multiple angles, which is really necessary to get an idea of how complex the shape is. Fortunately there’s a sweet spot that allows just the right distribution of weight so that it’s balanced and sturdy on the base.

I didn’t do a rough draught for this one, which isn’t my usual process, but everything went smoothly anyway.

interlocking panel box

final interlocking panel box

Is there a shape (solid) which can be repeated 6 times and interlocks to form a hexahedron? I’m still not entirely sure. This may even have search results, but I never looked it up. I wanted to figure it out for myself.

I mean, I still haven’t figured it out, but I got kind of close.

Continue reading “interlocking panel box”

self portrait practice

Here’s an art challenge to everyone: get better at self portraits. Here are the rules:

  1. Time limit is 15 minutes.
  2. Paper size is sketchbook size (roughly letter size).
  3. Sketchbook must be held in hand while standing up, looking into mirror.
  4. Use only a pencil and an eraser (nothing fancy).
  5. Start with toned paper which does not count toward your time limit.
  6. After time limit, write one new observation about the process on your drawing.

I used this as a warm-up exercise for my high school students in advanced drawing,  and everybody got better.

This was partly inspired by a TED Talk by Matt Cutts on trying something new for 30 days – mostly the idea that you can pretty much pull off improving at anything you try for 30 days.

As a challenge, there is one extra rule: post your progress somewhere on the internet. Below are day by day scans of my progress.

current definition of art

components of an artwork

A work of art has been fully realized when an artist actively participates in the actions of creating, shaping, and framing. When only one or two actions have been done, this only means that the artwork is not as fully realized as it could be.


Since ideas can exist independently of things, there are no physical properties associated with this action. Creating an artwork could be anywhere from having an inclination to make a particular thing to a deep meaning behind something.


Shaping is the rearrangement of raw materials in order to trade one system of organization for another.


The spatial and temporal boundaries which contain the work establish a frame for an artwork’s beginning and ending in space-time. The simplest form of framing is a change in perspective.


An assumption I make when using proportions in placement, repetition, size, and so on is that mathematical  relationships (such as the golden ratio) can be detected at a subconscious level and higher, and in this way are interesting to the viewer.

role of appropriation

When one artist uses another artist’s art, the former has had an active part in at least creating and shaping, and includes framing if the entire artwork was used. Examples of other people’s art (OPA) include photographing an uncited source, use of a font the artist did not create, and collage. My work seeks to be appropriation-free in order to maximize originality in the creative phase of art making.

torah stitch by stitch typesetting

to-engageThe nature of my involvement in this project has changed for the better. Putting my graphic design skills to use, I am now one of 3 typesetters for the project, and will be creating the diagrams which participants receive upon signup. I consider this to be a great honor and am privileged to have found a way to combine typography and Torah. There is a depth of personal meaning for me in this intersection.

If you’re wondering why the typesetting process involves more than just making sure all the letters are in the right order, there are many other considerations which must be made. In order to justify the columns, for example, one must use a combination of word spacing, kerning, and stretching certain parts of certain letters.

My stitching contribution to the project will continue as well, but I plan on slowing down in order to allow time to do typesetting.

Don’t forget to sign up to be a part of this incredible project.

torah stitch by stitch

This post should explain the images I’ve been posting on Instagram tagged with #torahstitchbystitch. I am part of the Torah Stitch by Stitch project, a global effort to create a cross-stitch embroidered copy of the Torah (the 5 books of Moses). Posting daily images of my progress keeps me from slacking off and hopefully will inspire others working on the project to keep moving forward.

Part of the project participation agreement is that you will try to document and share the process. My usual routine is to stitch at least one letter while I’m listening to music, sitting in my kids’ room as they fall asleep. I spend on average 20 minutes a night.

Read the info on the site linked above, but please ask me questions or give me comments (you can comment below this post). This is a very exciting thing to be working on and I would love to talk about it.

sphere of fifths

check out those shadows
check out those shadows

The circle of fifths is a music theory model several hundred years old which describes the relationships between diatonic scales. It can be seen as an illustration of infinite chord progressions. Sphere of Fifths uses the idea of infinite knots to represent musical cycles, and uses pentagonal knot designs of varying complexity to bring the music theory model into 3 dimensions. When the light source is changed to different angles, shadows from the opaque parts of the glass recombine in complex shadows; the viewer of the piece gets to decide on some of its content by taking this into consideration.

The piece appears to be held together tenuously, the same way a motive in a good piece of music will hold everything together without having to overshadowing things. The wood and strings are reminiscent of orchestra instruments. The knots themselves are similarly suggestive, and not directly representative of a circle of fifths diagram.

the rough draught with a thumbs up from the artist
the rough draught with a thumbs up from the artist

This piece was donated to the KJDS‘s 2014 fundraising event, Some Enchanted Evening.