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
This is an animation based on toroids, and what happens when circles of circles go in circles of circles: an image of endless four-dimensional convergence.
This is how it came about…
This is a set of visualisations which are all, in one way or another, based on pairs of interacting sine waves.
It turns out you can do a lot with sine waves…
This summer I went travelling around the Iberian Peninsula, partly because I had some of my work accepted for the exhibition accompanying the 2011 Bridges Conference on connections between art and mathematics, in Portugal – specifically, a large print of my generative art still ‘Vortical‘ and my interactive installation based on waves, Kenneth (see the visualisations it works with here).
Since I planned to travel all over Spain and Portugal carrying this thing, I figured I’d better make something more portable than the beautiful fire-engine-red box that Tom Hardiment made me for Kenneth Mark I, which was originally a solid hardwood drawer. I took the opportunity to give it a completely different aesthetic.
I was always torn between two looks for controls for my animations – either they should be hyper-futuristic, like a starship control panel, or stained wood and brass like the machines and instruments of the Victorian era. I have always had a thing for antique scientific equipment, so I can understand why steampunk has become such a big thing. I decided to go with wood and brass.
Interactive animations need intuitive controls to make them easy to play with. Since they always have a bunch of parameters to control, dragging with the mouse always seems a bit clumsy.
I figured that what’s really wanted is a bank of sliders and buttons to play with, each controlling a parameter. That way people can walk up to the controls as if they were approaching the bridge of a starship, and just twiddle them however they feel.
Now, with the help of the Dorkbot Alba team, I finally have the controls I’ve long dreamed of, in the shape of a box with six sliders, five buttons and two glowing switches. It is a thing of beauty.
The obvious next step once you have a good interface for a set of generative animations is to start putting them in public places for people to experiment with, I think. (more…)