Space as something to control on a two or three dimensional picture plane is such an exciting thing to me. Pattern, when obvious, makes images beautiful and understandable. Pattern organizes the chaos of life. Pattern creates expectations on the picture plane, and organizes a visual statement.

This organization of pattern was found at my local flea market. The alternation of the three elements made the participants (roosters, rabbits, and green peppers) look like a picture book image. Their placement is intentional. Their space is calculated as if on an artist’s canvas.

Below is another calculated mass from the local flea market. This is an outdoor space heater, made more efficient and beautiful with the inclusion of the patterned washtub from the interior of a washer. Perfect re-purpose, I think.

Pattern can be very regular and regimented, as in the above, or the artist can play with the least amount of pattern necessary to establish it, and then break it. Below is a recent embroidery. The size is about 9″ x 6″. Pattern is local in several areas: established, and then broken.

This piece was done in reaction to the “retablos” style of work from Mexico. In this form, which is small and usually on metal (of course mine is not as it is an embroidery), an accident is depicted, a narrative describes the accident, and the victim’s name saint hovers in the air viewing the scene.

This is why you and you and I am me. I never would have noticed that pattern in the caged animals (I would have been too pissed off at animals in cages) but you are right – it is gorgeous.

Curiously, mathematics is essentially the study of patterns and more significantly, the study of how two or more patterns relate, connect, explain each other. People who understand neither of our subjects (your art, my mathematics) never imagine they are connected. They view art as only creative and math as only rigid and conforming. Just a thought…

I wish that math had been explained to me in this way 50 years ago. I also love the idea, and does this have a parallel in math, of relief against activity?

Years ago, I came upon a charming sequence in a psychology book which offered a hint to finding the next number in the sequence:

1, 3, 7, 12, 18, 26, 35, 45, 56, ____

The hint was: Think of the figure-ground relationships in Escher’s lithography!

(BTW, the next number is NOT 68)

I have used this sequence for many years with many students and when you see it’s charm, Lee, I have a feeling you might find room in your curriculum to mention it as well.

PS Branny, zip it.

OK, I tried to use as much math brain power as I have to solve your question. I even googled it, and got answers! But they made my head spin, and I just hate that feeling very early in the morning. I know this must be involved with the Fibonacci series, and the Golden Section, and the figure and ground must change places. Damn if I can predict the next number!

You are braver than most, Lee, just for messing with it. I hope your readers do too. It’s not actually Fibonacci or related to phi (the golden ratio). But while we’re on the topic, both were of interest to Leonardo of Vinci.

It does related to Escher, as the cryptic hint in the psyche book indicated.

The next number is 69. Here is why: To go from number to number, you simply add 1, 2, 3, 4, 5, 6, etc, EXCEPT if the number is IN the sequence.

So we start with 1, but dont add 1 (cause its in the sequence), add 2, get 3, but dont add 3 (bc it is in the sequence), add 4, get 7, add 5, get 12, add 6, get 18, but DONT ADD 7 (bc it is in the sequence), add 8, get 26….and so on.

Said another way: Here are the DIFFERENCES between the numbers: 2, 4, 5, 6, 8, 9, 10, 11, 13, etc. The very numbers NOT in the sequence!

We simply dont add the numbers already in the sequence. Perfect figure-ground relationship. When the pattern becomes the background and the background becomes the pattern. Brilliant. Just Like Escher. 🙂

Showed your comment to a student today, a math-head. She looked at the sequence, understood it immediately, and blew the top off my head. Going to give her some extra credit if she will discuss this when we get to scale and proportion in our class. She will be so surprised!

Wonderful instructional comments, Lee. I like that you can do the art work, silently as an artist – and you can articulate what you have done factually.

Its the teaching part. Its not enough just to know; you have to be able to explain it. Thanks, Harry.