Oolong’s Playground

The Chrono-Synclastic Curlicue Clock shows three Curlicue fractals, corresponding to the current hour, minute and second of the day. With practice you should be able to tell the time with it – every time of day is associated with a specific shape of Curlicue.

At particularly notable times of day, the Curlicue dramatically simplifies, either by folding right in on itself, or reaching way out towards infinity. This is because the complexity of the seed, expressed as a continued fraction, relates to the complexity of the corresponding Curlicue. You can see this happen with the red-orange ‘second hand’ curlicue at various points throughout each minute. The longer-cycle fractals take longer, but they move about as fast because they show more of the fractal form. In the build-up to six o’clock, you can see the blue ‘hour hand’ curlicue spinning ever-inward, folding further and further in on itself, until at the exact moment it turns six – when the seed of the fractal is precisely one half – it collapses to just two points.

The most complex forms come when the seeds are irrational.

Here is another version. It has just one curlicue on a 24-hour-cycle, together with standard clock hands.

‘Chrono (kroh-no) means time. Synclastic (sin-class-tick) means curved towards the same side in all directions, like the skin of an orange.’
– A Child’s Cyclopedia of Wonders and Things to Do