Bare Bones Lessons: Stochastic Painting

I have always been interested in the notion that much of art is created by chance. A lot of people seem to think that they can’t do art because they don’t have the necessary skills or the time to learn them. We know those are excuses, that if anyone wanted to do art they would. But how much skill is involved in a particular piece and how much occurs due to chance is debatable. “Chance” here could be related to subconscious manifestations of our deepest fears, or it could be that your two-year-old knocked over your bottle of paint on an otherwise immaculate fruit-bowl portrait. I read this article called Chance in Art by Kristin Brenneman, a former Dartmouth student, and modified her instructions for a Stochastic Painting to be something better suited to a 7th grade art-infused math class (or math-infused art class). Here is what I came up with:

Driving Question: How can we employ concepts of chance to create new art?

Subjects: Math, Art

Materials: Blank paper, pencil, paint.

Choose a method to help students randomly generate a set of ordered pairs. Here is my list that I got from this handy random number generator:

  • Set 1: -5, 6
  • Set 2: -9, 2
  • Set 3: 2, 8
  • Set 4: 2, 10
  • Set 5: -4, 0
  • Set 6: 3, 7
  • Set 7: 0, 3
  • Set 8: -8, 10
  • Set 9: 7, 10
  • Set 10: -5, 0

Take your paper that you are going to paint on and estimate an xy-axis in the center that is roughly scaled. Since you are randomly generating lines, you don’t need to use graph paper and have exact measurements. This is art, not a scale drawing of a landscape design.

Next, you will need to decide on a rule for how to deal with this list. Here is the one I used but you could approach it differently depending on which kinds of math concepts you want kids to practice: The first set is the point in the cartesian plain, (-5, 6). Each subsequent set is the slope of the line segment starting at the previous endpoint and ending wherever you want (another way that you could do this is by choosing the first number to be the length of the line and the second number to be the angle after multiplying by 15 degrees. You could come up with others).

Now that you have a bunch of lines on your paper, choose one paint color to trace the lines, but don’t trace them exactly, use curves. Connect the curves until you have some kind of form. If you want, take a step back and see if you see anything in your form. Add other colors to fill in and embellish to give your form meaning if you wish. Or, if you prefer it to be completely abstract, that is great too.

When I did mine, I alternated the way I created my ratios for the slope so that sometimes it was the first number in the set divided by the second and other times it was the second divided by the first. I painted my lines green, started filling it in, and eventually saw a bird. Then I added some feathers and some other features, and this is what came out:

John's bird

I helped my kindergarten son by graphing the lines with him (he’s not really ready for dealing with cartesian coordinates too much yet) and then let him fill in what he wanted. He said that his is a camel:

Xavier's Camel

Let’s put art back into math class!

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