Fields · Study 005
Thread and Nail
Wrap 260 nails around a circle, join each nail n to nail n times k, and watch cardioids and nephroids bloom as the multiplier k slides.
What you're looking at
Number the nails 0 to 259. For a multiplier k, a thread runs from every nail n to nail n times k, wrapping around the circle. At k = 2 the threads envelope a cardioid. At 3 you get a nephroid, and each whole number adds another lobe. Between whole numbers the figure shears and reorganises.
The idea behind it
These curves are envelopes: no single thread is curved, but together their edges trace one. The same cardioid appears as the bright caustic inside a coffee cup, where reflected light rays play the part of the threads.
Try this
Move the pointer left and right to choose the multiplier from 2 to 12 yourself.
