Saturday, September 17, 2011

Permutations and Combinations

Permutations and Combinations
I have been homeschooling my son these past 2 years.  We are learning algebra together and got to Chapter 11:  permutations and combinations.  These have to do with the total number of possible combinations of lots of options.  Imagine how appealing this is and overwhelming!  Combinations allow for any set of choices from each set of options.  In permutations, the order of making choices is significant.  For example, if you have 4 choices of paint for a room.  One is the background color, and the other 3 will be used to stencil on top of the background color.  Not all options are available because you can't choose to stencil the same color as the background color (it won't show up!).  This makes it a permutation and is calculated differently.

Stacks of overdyed batik shapes
Well, I picked 13 colors, and dyed them in 3 different values, light, medium, and dark.  Then  I picked 3 different designs to either stamp out or draw with batik, in each color.  Up to now, there are 13 colors times 3 color values times 3 designs.  You can see how the numbers are starting to build up. My goal?  To overdye each possible combination in ALL the other possible color choices.  This step is a permutation, (which I could probably calculate now).  Well, except that my artistic side kicks in and I reject some of the possibilities for rather idiosyncratic reasons.  Regardless,  I thought the end result would be both interesting, but also very fun to play with making a number of new quilts. And as overwhelming as the entire project seems, each step was rather independent and I was able work in rather small increments of time.
A fat quarter of batiked fabric, the dark flowers are the wax.

The process involves bleach discharging all the fabric.  None of the discharged fabric goes all the way back to white, each is all discharged to very slight and pale as possible color.  Overdyeing is a transparent process.  It makes a difference what the underlying color looks like.  I took all the samples, cut each individual apart with a rotary cutter.  Then I reshuffled the samples into stacks of colors that I planned the overdye.
Stacks of fat quarters waiting to be cut into individual pieces
Stacks of all the shapes, in all the colorways, waited to be resorted for overdyeing.
Stacks of shapes in their new color piles awaiting the dyebath.
The fun part is the actual overdyeing.  Lots of unexpected and new colors pop up.  Last step is the boiling out of the wax.  It is hot and exhausting, but rewarding.  Dyeing is not always about getting what you thought you wanted.  I have been dyeing for years and I still get unexpected results.  This time, many of my colors did not go as dark or bold as I thought I was making.  And it's too late once you boil out the wax to overdye again.  There are so many variables that sometimes you just have to let go and accept what the dye does.  I didn't get what I was expecting, but what I got is simply beautiful and it all goes so well together.  I can see that I will be having lots of fun playing with all these samples!

One stack of shapes after it's red dyebath and after having the wax boiled out.


Diane Perin said...

What a fun ( if labor intensive) project! As another home schooling mom I am delighted to see how your child's schoolwork is making creative sparks for you.

Kathy York said...

Thanks Diane,
Sorry, what happened was pure coincidence. I had already started this project when we got to the Algebra chapter. I just didn't know it was called a permutation. It made an excellent teaching example for my son though!

Lisa Chin said...

It is fun to see how Algebra can be applied in real life! If only I had had these examples in school. Well maybe I still wouldn't have paid attention. Hahaha We will never know.

Thanks for showing all of your beautiful pieces. It is amazing how much work can go in to a very "simple" piece of fabric.

Kathy York said...

Thanks Lisa! I think Algebra gets a bad rap. It is about the math, but it is also about a way of thinking that is helpful in life, even if you didn't realize it was algebra that got you there. And, it is amazing to me how much work I am willing to do to make something that looks so simple (I think I might have it backwards! ha!). Thanks for your compliments!