Have you ever seen a digital sundial? There are a number of different types. Some use fiber optic cables to route sunlight into numbers, others use holes in panels to create "Poem for a Day". Some have drilled holes in blocks and others create digital sundials using layers of slits and masks.
As reported in the ArchDaily.com website on 23April 2016 by Patric Lynch, the design group Prescription in conjunction with Arup have developed a sophisticated sundial based on the analemmic path that the sun travels throughout the year. The classic "8" shaped analemma is made into a cone (think of someone stepping on an ice cream cone) and repeated with esthetic cutting of the cone top for each hour. At the bottom of the cone is a stenciled hour number and the angle of the analemmic cone only allows sunlight to poke through the stencil for the appointed hour.
The original prototype of this dial was made of flexible plastic through a 3D printing process. Prescription believes that "...the design is 100% scalable; the designers foresee applications for the design in both park and festival pavilions and home installations..."
A video of this analemmic sundial by Grisha Zotov can be seen at https://vimeo.com/161675472
French inventor and maker of things Julien Coyne of Mojoptix has created an intriguing digital sundial gnomon that can be 3D printed. His software design (dated 13 October 2015) uses the 3D open software OpenSCAD described as "The Programmers Solid 3D Computer Aided Design Modeller".[http://www.openscad.org/about.html].
Hines Digital Dial with light moving across optical fibers to create numbers
Steve Hines developed the first true digital sundial in 1984 routing illuminated optical fibers in a cylinder to 7-segment numbers display hours and minutes. Ultimately he received US Patent 4,782,472 on November 1, 1988 for a “Solar Clock with Digital Time Display”. Steve is an inventor of many optical devices, but as he recalls, “Sundials had not been a strong interest of mine before I started this project. I knew that there were analog sundials on horizontal and vertical surfaces, with the gnomon having to be parallel to the earth’s rotational axis. However, I wondered if it would be possible to create a true digital sundial with a display made up of 7-segment numbers like on a clock radio. By defining the problem as an optical analog-to-digital converter made it all the more interesting, suggesting further uses beyond being a clock.”
In the late 1980’s and early 1990’s several interesting articles appeared in mathematical journals discussing the possibility of fractal and digital sundials. The works of Manfred Schroeder  and K.J. Falconer  describe Cantor-like fractals embedded in a higher dimension.
Schroeder, in his article on “Fractals, Chaos, Power Laws” (1991) described a set of Venetian blinds: “[The ] idea underlying digital sundial is a set of bars that casts very different shadows depending on the direction of projection.”
Ultimately both Schroeder and Falconer imagined a multi-dimensional object, that when projected along one axis, casts a shadow, but when projected along another axis, shows only light with a “weightless” shadow. Although the mathematical principle is correct, the implementation is vague. As Schroeder stated, “...of course, the shadow-casting set is likely to be rather complicated, and the inventor understandably refrains from detailed instructions for its construction…”
Digital sundials have captured the imagination of many people, including cartoonists such as Wiley’s secret of Stonehenge shown below, which correctly displays the shadow bounds of the vertical stone gnomon. Two sundial enthusiasts who took Stewart’s article seriously were Robert Kellogg and Daniel Scharstein. Working independently, they both created and patented digital sundials that emulate Brother Benjamin’s mythic fractal sundial. Kellogg and Scharstein received nearly simultaneous patents, separated by only three weeks.
Jiyeon Song is a very talented media designer who created the One Day Poem Pavilion where here messages flow slowly by on the ground because they follow the movement of the sun. Jiyeon reflects “these slow messages offer the audience time to meditate. We cannot force it to go fast. We should wait. We live under the laws of nature. Slowness affords us time to rethink our lives which are finite and valuable. While the poem is revealed slowly, the meaning will resonate with the audience.”
Voshart's Digital Cube
Chindōgu is the Japanese art of inventing ingenious things that are, well, Rube Goldberg. Daniel Voshart from Toronto has designed a solar time-telling cube from 59 stacked millboard plates. [See: Voshart Cube ] The result is a digital sundial, though not as universal as those patented Hines [USP 4,782.472], Scharstein [USP 5,590,093] or Kellogg [USP 05,596,553] but still, it is an interesting dial.