How to teach your kids to draw fractals

It’s probably one of the best things that computer-geek dad/mom can teach their kid – to draw fractals with LOGO. Here is how you do it:

1. Install Kturtle or similar LOGO software
2. Refresh your knowledge on fractals (for example, at the excellent website of Jeffrey Ventrella)
3. Look at the examples of turtle graphics and fractals on the Internet
4. Repeat (together with your kid) very basic stuff from geometry: how to add/subtract angles, triangle postulate, etc.

Then fun begins:

• 30 minutes exercise implementing Koch Curve
• 1 hour exercise implementing Sierpinsky Triangle
• 1.5 hour exercise implementing various fractal trees
• 1 hour implementing Dragon Curve
• etc. etc.

Some very important things to remember:

• don’t overload your kid with knowledge. It’s important to get to exercises ASAP, otherwise motivation is lost.
• at first do every exercise yourself, without the kid. This way you make sure that you understand the goals and methods of implementation and can deliver that understanding to a kid.
• be clear at formulating goals and algorithms, show on paper how stuff works.
• don’t try to be overly supportive, give a kid space to think and experiment with implementation.
• ask kid questions and stimulate thinking: “what about changing this parameter here, how will it affect our fractal”?
• don’t try to do all exercises at once – this would not be effective, since the brain needs time to digest new concepts.

This could be the beginning of your kids’ big love – love to mathematics and science.

Illustration: Sierpinsky Triangle, created by my daughter with Kturtle:

The source code:

	learn triangle $x {
	fw $x
	tr 120
	fw $x
	tr 120
	fw $x
	tr 120
	}
	learn serpinsky $x, $level {
	triangle $x
	pu
	fw $x/2
	tr 60
	pd
	serpinsky1 $x/2, $level
	}
	learn serpinsky1 $x, $level {
	if $level == 0 {
	return
	}
	triangle $x
	pu
	tl 60
	fw $x/2
	tr 60
	pd
	serpinsky1 $x/2, $level – 1
	pu
	tr 60
	fw $x
	tl 60
	pd
	serpinsky1 $x/2, $level – 1
	pu
	tr 180
	fw $x
	tl 180
	pd
	serpinsky1 $x/2, $level – 1
	pu
	tl 60
	fw $x/2
	tr 60
	pd
	}
	$level = 7
	reset
	go 120, 0
	print "Serpinsky carpet level " + $level
	pu
	go 0, 400
	pd
	dir 30
	serpinsky 400, $level

view raw

sierpinsky.turtle

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