Patterns Inside Patterns

💡 The idea

A block built from a block built from a block: self-similar patterns from three tiny definitions.

• Self-similar means the small parts look like the whole.
• Each level uses the level below it as if it were a single command.
• Every level must finish where it started, or the levels drift apart.
• This is the idea behind recursion, written out as separate named levels.
• Three short blocks can produce a picture that would take hundreds of lines by hand.

📘 Words to know

self-similar

the small parts look like the whole

recursion

a definition that uses itself

level

one layer of a pattern built on the layer below

👀 Watch this

Squares make a rosette, and six rosettes make a ring: one idea used at three sizes.

to unit
repeat 4 [ forward 20 right 90 ]
end
to ring
repeat 6 [ unit right 60 ]
end
to garden
repeat 6 [ ring forward 60 right 60 ]
end
garden

▶ Run it below

✍️ Your turn

1. Run it, then comment out the last line with # and confirm nothing draws.
2. Change only the unit, to repeat 4 [ forward 30 right 90 ], and see all three levels change.
3. Change ring to repeat 8 [ unit right 45 ].
4. Change garden to repeat 3 [ ring forward 90 right 120 ].
5. Explain why every level has to end where it began.

🎯 Challenge: Rebuild all three levels with a triangle as the unit. Predict how the whole picture will change before you run it.

to unit
repeat 3 [ forward 25 right 120 ]
end
to ring
repeat 8 [ unit right 45 ]
end
to garden
repeat 4 [ ring forward 70 right 90 ]
end
garden