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Step 9

A loop inside a loop

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A repeat runs the blocks inside it again and again. So what if one of the blocks inside is another repeat?

A square is a repeat of 4 sides. Now put that whole square inside a second repeat. The inside loop draws one square. The outside loop says “do that again”, and turns the turtle a little each time. Together they make a ring of squares from only a few blocks.

The rule to remember: the inside loop runs all of its laps every time the outside loop goes round once.

Try it: twelve squares

Open the frame and press Run. Look at the two repeat blocks, one inside the other.

Twelve squares: a repeat of 4 inside a repeat of 12. Open full size

Try it in TurtleLab: https://learn.porttack.com/turtlelab/?sample=lesson-nested-count

Before you change anything, work out:

  1. How many forward blocks run in all? (Think: how many sides does one square have, and how many squares are there?)
  2. After each square the turtle turns 30. Why 30?
  3. You change the outside repeat to 6. What turn closes the ring?

Then try it: 6 squares with a turn of 60, and 36 squares with a turn of 10. Last, predict what happens with 12 squares and a turn of 20, and then run it.

Check your answers
    1. The inside loop runs 4 sides, and the outside loop runs it 12 times, so 12 times 4 is 48.
  2. 12 squares times 30 is 360, a full circle, so the ring closes. It is the same rule as before: laps times turn must make 360.
  3. 60, because 6 times 60 is 360.

With 12 squares and a turn of 20, the turns add up to 240, only two thirds of a circle. The squares fan out and leave a gap instead of closing a ring.

A flower of hexagons

The same idea makes a flower. This time the inside loop draws a hexagon: 6 sides, turning 60 each time.

A flower: a repeat of 6 inside a repeat of 6. Open full size

Try it in TurtleLab: https://learn.porttack.com/turtlelab/?sample=hexagon-flower

  1. How many lines does the turtle draw in all?
  2. Change the inside repeat from 6 to 5 and the turn inside it from 60 to 72. What shape does the inside loop draw now? To make a flower of five of them, what should the outside repeat and the outside turn be?
  3. You change both repeat blocks to 20. How many lines is that? Work it out before you try it.
Check your answers
    1. Six hexagons with 6 sides each.
  2. Pentagons. For a flower of five, the outside repeat is 5 and the outside turn is 72, because 5 times 72 is 360.
    1. A loop inside a loop multiplies: 20 times 20. This is why a few small numbers can draw a very detailed picture.

Which loop does what?

When you read a nested loop, ask two questions:

  • What does the inside loop make? (One square. One hexagon.)
  • What does the outside loop do with it? (Repeat it in a ring.)

Then check that the outside turn times the outside laps makes 360, if you want a ring that closes.

Make your own

Open TurtleLab in a new tab and build there. The frames above do not keep your work.

Make a ring of triangles, or of any shape you like, using a loop inside a loop. Pick the inside shape first and get it right. Then put it inside the outside loop. Work out the outside turn before you type it.

Then make it colorful: put a set color block inside the outside loop but outside the inside loop. Why does it change color for each shape, and not for each side?

Save your work

Press the PDF button to keep a copy of your blocks and your drawing.

Done early?

Open the Nested squares sample. It uses a loop inside a loop and a box. Find the box and work out what it does to each square. What does the Output box at the top right show?