# Recamán’s

Clock

The simplicity of Recamán’s
sequence belies the beauty of this complex pattern. From red, to
white, to blue, each arc spans a greater interval: the first, at the
very bottom, advances one step; the second, two steps; the third,
three; and so on… only once we reach the fourth arc does it
have the chance to retreat into a void.

And so it continues, only reversing if it lands in an empty slot,
otherwise marching eternally forward. Coincidentally, the resultant
spirals map to the idiosyncrasies of our timekeeping. Here, it
displays the viewer's local time.

## “Complications”

Tracking the blue spiral, an orbiting dial captures minutes much
like a regular timepiece with each of the twelve loops additionally
representing an hour—one can tell the time from a single
point. The 14-looped orange-white spiral has a similar dual meaning,
representing the hour of the day with its angle and the day of the
week with its loops. The peculiarities of the sequence dictate that
hours spiral outwards whereas the week circles inwards, with
midnight Monday at the very top.

The lunar phase tracks upwards along the lone white arc, while the
sun's position is mirrored on the outside of the double-looped
orange spiral—taking a full day to complete a single
revolution. The sun rises in the “east”, reaches its
zenith at noon, and sets to the “west” over the horizon
of the overlapping spiral.