Fractal Tree

"What is a fractal?"

A little girl looks at me, with questions in her eyes. She's cute as a button, much cuter than the rest of my customers at the faire, but the question and the blank stare that greets me when I tell them that I do fractal art is the same.

"Well," I say, pointing at my pictures. "This is fractal art."

"Oh. COOOL!" She says in that ten-year-old tone reserved things made of pure awesome, like new comics books or particularly large squishy worms. The next question comes.

"How do you make them?"

How am I to answer? I've tried different explanations throughout the day. When I say "Linear Algebra," eyes start to glaze over and wander away. "The Chaos Game," is met with a wise nod and smile that says, "I don't know what you're talking about, but it sounds cool." "A program called Apophysis." satisfies many, but frustrates me, because telling the program is like a painter saying they did it with a brush- sure, that's how I did it, but not really how. It's one of those statements that seems to say everything but really explains nothing.

Besides. She's 10. She wants to know the heart of the matter. Complex math can wait until, say, twenty.

So how to I capture the heart of a fractal? I gaze off into the forest, groping for answers.

Inspiration strikes like a bolt of lightning to the tallest tree.

"Imagine a tree," I say.

"Uh-huh?" She says.

"Got the tree in your head?" I say, smiling encouragingly.

"Yes!" she fires back.

"All right." I say. "Break off a branch of the tree, stick it upright in the ground. What does it look like?"

Her face screws up in thought. After a second she says, "A tree."

"A smaller tree." I agree. "Now, take that tree, break off another branch, stick it in the ground." I say. "What does it look like?"

"A smaller tree!" She says triumphantly.

"Yep!" I say, grinning. Such enthusiasm should be rewarded with a smile. "Now. Take that tree, and break off a branch of it, stick it in the ground again. What's it look like?"

"A smaller tree!" She says, not smiling anymore. She's beginning to get bored.

"Yep!" I say. "So. That tree is made up of branches that look like a tree. That branch is made of branches that look like a tree. What's a tree made of?"

She stops. She has to think about this for a little while.

"Smaller trees?"

"Yep!" I say. "And when something is made up of smaller copies of itself, that's a fractal."

"Oooh!" She says. "COOOOL!" In that ten-year-old tone reserved for new comic books, really icky long worms, or, apparently, fractals.

She smiles at me and skips her way into the crowd.

Note: This explanation works particularly well for ordinary people. Math majors, computer science majors, engineers, and tech nerds in general either think WAYYY too literally or way too hard about it. "It's a branch stuck in the ground." "It's a stick" "It's a twig." "It's a binary tree." "Is this a trick question?" NO! It's just a smaller TREE!

This is .gif animation, so download it to see the glory.