Fourier Drawing

Draw any shape and watch spinning circles redraw it.

0/2challenges

40 circles

Circles

Speedcycles/s

Circles used: 40 of 256
Shape energy captured: 100.00%
Largest circle: 118.4px

The model

Any closed curve can be written as a sum of circles spinning at whole-number speeds: a Fourier series. The shape is sampled at 256 points, turned into complex numbers x + iy, and a discrete Fourier transform gives each circle's size and starting angle.

Circles are sorted biggest first. A handful already give the outline; sharp corners need many more, because a corner is made of high frequencies.

Try this

Pick the square and drop to 5 circles: it is round. Push to 100 and the corners come back, with a little overshoot at each one: the Gibbs phenomenon.

Exact discrete transform of the sampled curve; resampling evenly by length first. Educational model, not an engineering design or validation tool.

Achievements0/2

Doodle +20Draw your own shape and replay it with circles.
Less is more +20Recognisably draw a shape with 12 circles or fewer.

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