Draw with mouse or finger. Changing the fold count re-maps whatever you've already drawn, so try it after a few strokes.
About this
David Brewster patented the kaleidoscope in 1817 after noticing something about a pair of angled mirrors: light bouncing between them doesn't just reflect once, it reflects off the reflection, over and over, until the original scrap of coloured glass has been copied all the way around a point. The number of copies isn't a matter of taste — two mirrors set at angle θ produce exactly 360°/θ of them, no more and no fewer, because each bounce is a rigid rotation and rotations by a fixed angle either tile a full circle evenly or never close up at all.
That's the whole trick, and it needs no glass to work: pick a centre, pick a fold count
N, and copy anything you like by rotating it 360°/N at a
time. Add a flip — a mirror reflection — between each rotation and you get twice
as many copies and the left–right symmetry a real two-mirror kaleidoscope has. Mathematicians
call the full set of rotations and reflections that leave a shape looking the same the
shape's dihedral group, written DN; it's the same bit of structure
behind a starfish, a stop sign, a snowflake and the sikku kolam drawn at a doorstep every
morning across Tamil Nadu.
Because the fold count is applied at the moment of drawing rather than baked into the strokes, nothing here is fixed once you've drawn it. The same scribble reused at fold 4 looks like a pinwheel; the identical scribble at fold 12 looks like a flower with no pinwheel left in it anywhere. Turn the mirror off and the pattern keeps its rotation but loses its reflection — a subtler kind of symmetric, the kind a spinning propeller has but a snowflake doesn't.