"A treasure hunt to make a drawing"

My eight-year-old friend Mani, who loves both math and art, was especially taken with the Sol LeWitt exhibition. One of LeWitt’s wall drawings and its instructions so inspired Mani that he went home and made his own drawing. He described LeWitt’s instructions – which might seem a little dry at first glance – as a “treasure hunt to make a drawing.” Here’s Mani’s account (mostly in his own words) of his art adventure:

Me: Do you remember what first interested you in that exhibition?

Mani: My mom said that the activities at the Walker on that day were about geometry, which interested me immediately. [T]he first thing I did was look at the “eight dots” drawing (“Wall Drawing #224”) The drawing is as big as a wall and contains eight points that are somehow related.  There are also instructions for each point printed next to the points. There are also some lines that Sol LeWitt used to help create the drawing.

What did you think of the instructions?

My first reaction to the “Wall Drawing #224” was that I was not very excited at all. Eight dots didn’t seem that cool. But then my Dad asked me to read the instructions for the eight points out loud.  I could follow the instructions for the first three points, but as I read, the more confusing the instructions got. I couldn’t even finish reading the eighth point out loud, because I was laughing so hard that I fell over.  “The eighth point is drawn where two lines would cross if the first were drawn from a point halfway between the seventh point and a point midway between the first point and a point midway between the midpoint of the bottom side and the lower right corner to a point midway between the midpoint of the left side and a point midway between…” Those were the instructions for point number eight! It was funny that he kept saying “the midpoint of the midpoint of the midpoint.”

Did it seem like a good way to make a drawing?

Yes because it’s like you’re giving somebody a treasure hunt to make a drawing, and it makes this wall with just eight dots on it seem pretty cool.

I saw your drawing. How did you end up doing that?

I started sketching the first 5 points at the exhibit, but stopped because I didn’t have a ruler. Then, at home, my dad challenged me to draw the eight dots. At some point I needed to draw lines along with the dots on the paper because all the points except the first few involved finding the intersection of two lines. When the instructions got difficult, I took a different sheet of paper and broke up the instructions into different sections, which helped me understand the instructions.

Were the instructions easy to follow?

Everything was easy up to point 3, points 4 and 5 were a little hard because they involves finding the intersection of two lines, but points 6, 7, and 8 were extremely hard because not only they involved finding the intersection of two lines but the lines had millions of midpoints in their instructions.

What was the most surprising thing about working on it?

It surprised me that the first and eighth points are surprisingly close. I wonder if it’s because their instructions are similar. I wonder what would happen if you took the midpoints of the eight points. Would some of the midpoints be in the same place?

Did you exactly follow the instructions or did you make your own variation?

I followed the given instructions, but I have an idea for a variation of a set of instructions. I’m planning to do it in Scratch! Take 4 points. Connect them with lines and find their midpoints. Connect the midpoints and find the midpoints of them. Do this 20-30 times until you see some sort of pattern.

[Note: Scratch is a programming language designed for kids. See scratch.mit.edu for more info.]