One of us, Maria, recently posted this on our Facebook page:

This is what I call “lap-ware”: a little beautiful thing you show a toddler who climbs into your lap as you work on your computer. Even someone who knows nothing about math can change, say, 2 to 3 in the formula and observe the (beautiful) results. Math experimentation for the w

And the other one of us, Yelena, tried it with her son. The results where exciting and unexpected.

The first thing that my almost 5-year old boy said when he saw the original graphics was **“Wow! Can I see it again?!**“. That sounded promising. So I told him that not only could he watch it, but he could control it and change it HIMSELF! Immediately he was eager to try his hand at manipulating the graphics. I showed him the formula and explained that it was a coded command, called a **function**, that he could control by changing one, two or three **parameters** and put his own numbers where the original 2, 2 and 0.7 were.

First, he replaced the first two numbers only and kept the third one, 0.7, the same. He tried 1, 3, then 7. Then, as he was about to try plugging in 4, I asked him what he thought the result was going to be. Was it going to be flat, similar to what he got when he put 1 into the equation. Or was it going to be all scrunched up and spiky like when he used 7. After a bit of thinking, he predicted that, although **the result wouldn’t be flat, it wouldn’t be as “wrinkled” as the result he got with 7**. Even though his prediction turned out to be accurate, he was more thrilled with the ability to check his prediction than with the accuracy of the prediction.

Next, he wanted to plug in more different numbers. So we tried ages of all the family members, including our cat. In the process, I noticed that some of us were** squares** and others – **triangles** (depending on whether our age was an **odd or an even number**). This led to **lots of giggles** as we were trying to figure out who was who in our family.

As we plugged the number 100 into the formula (the age of a tree outside), something wonderful happened. My son looked at the graphics and exclaimed **“Look, Mom, it’s also symmetrical!”** And sure thing, it was.

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