Math Playground
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Symmetry artist

Paint with a mirrored brush. Whatever you draw in one slice gets repeated and flipped — a kaleidoscope on a touchscreen.

Symmetry artist

Paint one slice — a kaleidoscope appears. Move the slider to change the number of mirrors.

6
6

What's going on

Every dot you place gets copied to all the slices around the circle — and each copy is also reflected. That's dihedral symmetry: rotations and reflections, which together give the strong kaleidoscope feel.

Try this

Set the slider to 6 mirrors and draw a single petal. You'll see a snowflake. Try 12 mirrors and draw a small squiggle — a stained-glass window appears.

Where it shows up

  • Snowflakes — six-fold dihedral symmetry.
  • Mandalas — usually four-, six- or eight-fold.
  • Stained-glass rose windows — typically twelve-fold.
  • Many flowers (daisies, lilies) — five- or six-fold.