The Horizon Dial

This is a new (2022) display design intended for use on wall-mounted clocks and digital watches with color screens, created by Jeremy Bornstein and James Home. The goal is to be easily readable (with a bit of practice) and also not to scream HEY I AM A CLOCK YOU NEED TO KNOW THE TIME, because that is often annoying.

This design was partially inspired by the set theory clock, in that it is an alternate method for displaying the precise time on a digital clock. Our design is somewhere between a first principles design and recycling of useful concepts from existing clocks.

Basics

The clock is divided into four sections with two perpendicular lines in the form of a plus sign (+). This is remeniscent of a normal clock face which often has markings at top, bottom, left and right. However whereas a normal clock face is a 12-hour display and makes two complete rotations every day, ours is a 24-hour display and only rotates once per day.

More significantly though, this clock does not have hands which rotate in any continuous fashion (except for the seconds display, which we'll get to later). Rotationally speaking, we have only four orientations, indicated by the position of the illuminated (currently in yellow) portion of the central +. As an example, check out how the clock looks at high noon:

You can visualize the yellow ray pointing up at the sun, which is notionally overhead at noon.

Note that the bottom half of the clock is colored in shades of brown, and the upper half in blue. The brown represents the earth, and the blue represents the sky.

Similarly, if the sun is on the other side of the planet, it's midnight:

Midway between midnight and noon we have 6am and 6pm (18h or 18:00 in 24-hour notation). One of the rotational aspects we keep from traditional clock faces is clockwise rotation, so moving from midnight (yellow ray down) to 6am means that the illuminated ray points to the left:

...And moving from noon to 6pm (18h) means that it points to the right:

The actual hour

The four possible illuminated rays only get us four hours of the day, which isn't enough to give us all 24 hours. When we want to indicate a number of hours after the hour indicated by the illuminated ray, we add an indicator in the quadrant immediately clockwise from the ray. Since each quarter of the day has six hours in it, and an empty quadrant indicates the first of those hours, we need some way of marking the second to the sixth hours. Here's what 1pm (13h) looks like:

That's just a simple square. Note that it's in the quadrant clockwise from the illuminated ray. Next we'll add another square to indicate the next hour, 2pm (14h):

You don't really need to memorize these shapes by the way: just count the number of segments present. The first three segments are squares, so it's extra easy. Here's 3pm (15h):

Notionally speaking, we have one empty square left in the quadrant, but we have two more hours to indicate. The fifth hour (4pm/16h in this case) is represented by adding a triangle as follows:

And by now you can guess what the sixth hour looks like: we add another triangle to fill the empty space, ending up with a square that more or less fills the quadrant. In this case, 5pm/17h:

Take that and rotate it...

Remember that the position of the hours indicator is always relative to the illuminated ray. Check out the clock faces for midnight, 1am, 2am, 3am, 4am, and 5am:

The clock faces for 6am to noon are exactly like those, rotated 90° clockwise:

I haven't illustrated 6pm to midnight but I think you get the idea now.

Minutes after the hour: tens digit

We are a digital clock, so the next aspect to represent is the tens digit of the minutes after the hour. Since there are 60 minutes to the hour, we need six values. We already have a way to display the numbers 0 to 6, so we'll use the exact same shapes as we used for the hours. Here's what the face looks like at 12:00, 12:10, 12:20, 12:30, 12:40, and 12:50:

Note that these indicators appear not in the quadrant immediately clockwise from the illuminated ray—which is occupied by the hours indicator—but in the quadrant immediately clockwise from that.

Minutes after the hour: ones digit

We're almost there. The next thing we need to show is the ones digit of the time. For that we need a full complement of the digits 0 to 9. Fortunately, we have two empty quadrants and shapes that we can use. For the ones digits 0 to 5, we only need the next clockwise quadrant. Here's what the clock face looks like at 12:00, 12:01, 12:02, 12:03, 12:04, and 12:05:

Now we've run out of space in the third quadrant, but we just start using the remaining one, leaving the previous quadrant with the full square that represnts 5. So to represent 6 minutes after the hour, we put a 1 in the final quadrant, and for subsequent digits, we just keep incrementing the number in the final quadrant. Here's 12:05, 12:06, 12:07, 12:08, and 12:09:

Wait a second!

The seconds display is another element very similar to traditional clock faces. In our case though, it starts wherever the illuminated ray is. Here's a sequence of clock faces illustrating midnight through to 00:01 in ten second increments; note that zero seconds is at the bottom, to match the downward-pointing illuminated ray.

That's It!

Now you know how to read the clock by putting together all of the elements described above. Here are a few examples (with no seconds shown for simplicity) for verifying your understanding and for practice:

7:34am 9:10am 2:40pm
2:12pm 5:55pm 7:23pm
10:09pm 3:04am 5:18am

This is a work in progress and your comments would be appreciated.

A live clock showing the time according to your browser is here.

Thanks for reading! -Jeremy