Patterns are not just something we draw on squared paper. Look closely and you can find them in wings, leaves, shells, flowers, buildings, fabrics and works of art.
In this lesson you will first become a pattern detective, looking for mathematical rules in the world around you. Then you will use those same ideas to design mathematical artwork of your own.
What rule can you see?
When you look at a pattern, ask: is something repeating, sliding, reflecting, turning, branching or tessellating?
Patterns in nature
Nature has a surprise for us: its patterns are often almost regular rather than perfectly exact. Make a prediction before opening each answer.
A living starfish may have five similar arms without every arm being identical. The mathematical idea is still useful even when nature introduces variation.
Patterns in buildings and design
People use the same mathematical ideas deliberately. Architects, artists and designers use repetition, tessellation, symmetry and turning to build complicated designs from simple rules.
Architecture photographs © Sumthing Else.
Use the transformations yourself
Can you guide the butterfly to the flower and make sure it finishes facing the right way?
Now become the designer
You have found mathematical rules in nature and in things people have made. Now use those same rules to create a piece of artwork of your own.
Choose one tiny motif
Draw one small asymmetric shape: perhaps a lightning bolt, fish, leaf, boot, arrow, letter or completely invented symbol.
Then ask: what happens if I slide it, turn it or flip it?
Your design brief
Your finished artwork must use at least two mathematical rules. The rules should be visible enough for somebody else to discover them.
Slide your motif the same distance in the same direction.
Turn your motif around a chosen centre.
Make a mirror image across a chosen line.
Repeat shapes without leaving gaps or overlaps.
Mix two rules
Repeat a motif along a strip, alternating it with its mirror image.
Build a design around a centre, then add mirror symmetry inside each section.
Tile an area, but turn the motif as you move from one tile to the next.
Grow a branching design on one side of a line, then mirror it.
Create, then test your pattern
You can use pencil and ruler, coloured paper, paint, collage, stamps, tiles or a drawing app. The material does not matter — the mathematical rule does.
Can someone reverse-engineer your pattern?
Show your finished artwork to somebody else without explaining the rules first. Ask them:
What is the basic motif?
What movement or transformation repeats?
Can you find a mirror line or centre of rotation?
Can you spot a second rule?
If they can uncover your rules, you have communicated the mathematics through the picture itself.
Go on a pattern hunt
Find five patterns around your home, street, park or museum. Photograph or sketch them.
For each one, ask: What repeats? What stays the same? Is the pattern exact or approximate? Could more than one rule be happening at once?
You found patterns — and made one of your own.
The same ideas can appear in living things, buildings, artworks and designs: repetition, symmetry, transformations and tessellation.
Lesson 5: Patterns in art, nature and design
Download the lesson handout and activities to explore patterns, symmetry and repeated structures in art, nature and design.
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