Kaleidoscope
A kaleidoscope turns a single stroke into a symmetric flower by reflecting it around a centre. Move the pointer over the canvas and this tool copies your motion into every wedge of an n-fold rotation, then mirrors each wedge, so one gesture blooms into a whole mandala. Choose how many mirror lines to use and the symmetry group shifts from a simple three-fold pinwheel to an intricate twelve-fold rosette; toggle the mirror reflection on and off to switch between pure rotational symmetry and full dihedral symmetry. Strokes are coloured by speed and direction and fade slowly so the pattern breathes, and any frame can be saved as a PNG. It is equal parts drawing toy and a hands-on look at the symmetry groups behind tilings and snowflakes.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- Reflecting a wedge as well as rotating it gives the dihedral group Dₙ, with n rotations and n mirror lines — 2n copies of your stroke; rotation alone gives the cyclic group Cₙ with n copies and a pinwheel that has no mirror symmetry.
- A real kaleidoscope with two mirrors at angle 360°/2n produces exactly this n-fold pattern by repeated reflection; the smaller the angle, the more repetitions you see.
- The same symmetry operations that fold your stroke here classify wallpaper patterns, snowflake arms (six-fold) and the rosettes in Gothic windows.
- Runs 100% in your browser — simulations are computed locally on your device.
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