Geometry Art III

Review — Lesson 6 5 min

• A star is a shape where the arrow goes round more than once.
• The spikiest star turns 180 − (180 ÷ points).
• A colour change inside the loop gives every line its own colour.

Quick-fire

Your polygon block turns the arrow all the way round. Which way does it face at the end?

Today’s Topic 3 min

• Draw a shape, turn a little, draw it again
• The copies rule — copies × turn = 360
• A flower (petals) (sides) (size) :: custom block that uses your polygon block
• Taking a wait out, because the drawing got too slow

Learning outcome

By the end of this lesson you will be able to:

1. Make a pattern by repeating a shape with a turn between.
2. Work out the turn that makes a pattern close up.
3. Build a My Block that calls another My Block.

Learnt — patterns that go all the way round 28 min

1 · One petal, then twelve

Draw one hexagon from the middle of the Stage. The arrow ends facing the way it started. Turn it 30 degrees and draw the hexagon again. Do that twelve times.

repeat (12)
  polygon (6) (45) :: custom
  turn cw (30) degrees
  change pen (color v) by (8)
end
            

2 · The copies rule

The pattern closes up when the turns add up to one whole turn. So: copies × turn = 360, or turn = 360 ÷ copies. It is the 360 rule again — this time for whole shapes instead of sides.

3 · A flower block

Wrap the pattern in a block with three inputs. Inside, it calls your polygon block — a block can use another block.

define flower (petals) (sides) (size)
repeat (petals)
  polygon (sides) (size) :: custom
  turn cw ((360) / (petals)) degrees
  change pen (color v) by ((100) / (petals))
end
            

Basic — a rainbow flower 24 min

Open your project. Keep the polygon block.

Step 1 — speed up the polygon

1. Find your define polygon hat.
2. Drag wait (0.1) seconds out of it and delete it.

Step 2 — the flower block

1. Make a Block called flower with three inputs: petals, sides and size.
2. Inside: repeat (petals).
3. In the repeat: polygon (sides) (size) :: custom, then the turn, then the colour change.

Step 3 — draw it

1. Under the flag: erase all, pen size 2, a pen colour.
2. Travel to x: 0, y: 0, facing 90.
3. flower (12) (6) (45) :: custom.

define polygon (sides) (size)
repeat (sides)
  move (size) steps
  turn cw ((360) / (sides)) degrees
end

define flower (petals) (sides) (size)
repeat (petals)
  polygon (sides) (size) :: custom
  turn cw ((360) / (petals)) degrees
  change pen (color v) by ((100) / (petals))
end

when flag clicked
erase all
set pen size to (2)
set pen color to [#ff4fa3]
pen up
go to x: (0) y: (0)
point in direction (90)
pen down
flower (12) (6) (45) :: custom
            

Three flowers

One block, three very different flowers.

• Top left: 8 squares.
• Bottom middle: 10 pentagons.
• Top right: 16 triangles.
• Each flower starts in its own colour and fits on the Stage.

flower (8) (4) (35) :: custom
flower (10) (5) (28) :: custom
flower (16) (3) (52) :: custom
            

A mandala

Layer three flowers on one centre to make a mandala — a round, repeating pattern.

• All three flowers share the same centre.
• The biggest is drawn first, the smallest last.
• Each layer is a different colour.

flower (8) (4) (68) :: custom
flower (12) (6) (30) :: custom
flower (6) (3) (26) :: custom
            

A flower made of stars

Use last lesson’s star block as the petal.

• Eight five-point stars, all from the centre.
• The pattern closes up.
• The colour moves on between stars.

repeat (8)
  star (5) (80) :: custom
  turn cw (45) degrees
  change pen (color v) by (12)
end
            

Plant a garden

Click the Stage to plant a flower. Every flower is a surprise.

• The green flag clears the board and plants one flower.
• Every click plants a flower where you clicked.
• Each flower picks its own petals (5 to 12), sides (3 to 6), size and colour.

when stage clicked
pen up
go to x: (mouse x) y: (mouse y)
point in direction (90)
pen down
set pen (color v) to (pick random (0) to (100))
flower (pick random (5) to (12)) (pick random (3) to (6)) (pick random (15) to (32)) :: custom
pen up
            

Summary 5 min

• Draw a shape, turn, draw it again — that is a pattern.
• The pattern closes when copies × turn = 360.
• A My Block can call another My Block.
• Scratch’s colour runs 0 to 100. Changing by 100 ÷ petals goes once round it.

Rotational symmetry

A pattern that looks the same after you turn it part of the way round.

Petal

One copy of the shape in a flower pattern.

Mandala

A round pattern built from layers that repeat around a centre.

Hand in

Save your garden. Next lesson the numbers move onto the keyboard, and your project becomes a pattern machine.