The National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA) is an Italian Government sponsored research and development agency. In 2017 Sara Bollanti and her team at ENEA in Frascati developed a solar compass that "is 100 times more precise than magnetic compasses..." with applications for surveying, civil engineering, and for us, sundial alignment. The heart of the device is a combination of GPS receiver for determining both time and geographic position and a solar collector consisting of a narrow slit and a CMOS image detector. Essentially this is an electronic solar azimuth compass. A smallArduino computer uses the UTC time plus geographic coordinates to compute the local sun azimuth and then compares it to the position of the sun's projection of a slit on a CMOS detector. According to ENEA, the "...electronic solar compass is compact, completely automatic, cheap, and reaches an accuracy better than 1 arcmin. The latter is one of the best currently available values, comparable to those achievable by means of much more expensive and sophisticated devices, like coupled GPS systems (see for example U.S. patent 5,617,317A, 1997) or gyrocompasses. Furthermore, the ENEA compass provides the orientation in a few seconds, a time extremely shorter than that necessary for gyrocompasses."
By 2018 this was tested in Antarctica and now the mathematics has been reduced to fit into your smart phone. In April 2020 the ENEA team announced the developed the smartphone app i called "SunPass". It is currently in beta testing and will soon be available at the Play Store. In basic form, the app allows you to acquire the sun azimuth by pointing toward the shadow of a vertical object such as a building ("shadow method") or the shadow of a vertical pole ("gnomon method"). A more accurate appraoch is to construct a box with a slit on the front and hole on top such that the smartphone can observe the illuminated sun line on the floor of the box ("Slit method"). For the advanced, one can construct a precision holder from a kit that mounts on a tripod.
ENEA's goal of a low cost, simple method of precision alignment is now accessible to all. This new technology implements the mathematics of determining the sun's azimuth in elegant ways. But of course it only works on sunny days.
Whether it be Delhi or Las Vegas, artist Daku brings shadows to life, creating words that slowing change their shape but never lose their meaning through the course of the day. As reported by mymodernmet.com, "As part of the St.Art festival, which curates public art in Delhi’s Lodhi district, Daku’s carefully realized [shadow] installation demonstrates the power of words. The artist, whose name means 'bandit' in Hindi, had been thinking about executing this project for several years when finally given the opportunity by the festival." The anonymous artist Daku told CNN, “I had to decide the size of the letters, the length of the pieces, and the angle I could place them in so pedestrians could easily see it.” mymodernmet.com concluded "The artist carefully selected which words to include—balance, order, reflection, future, seasons, space—each a reflection on movement, time, and change. Reaching its apex at mid-day, the letters slowly blur and dissolve, put to rest each evening before beginning anew."
The making of shadow writing in Las Vegas by Daku
Daku's cut-out words on the south facing walls of buildings is a clever implementation of sundial and involves a lot of subtle mathematics. Daku's lettering is placed on the wall horizontal to the ground, usually with very little change in the scale of the lettering. Mathematically the noonday lettering on the wall is lengthened by the tangent of the latitude plus solar declination. But the visible size of the lettering is foreshortened by the cosine of the upward look angle of the pedestrian on the ground.
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].
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.”
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.
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…”
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.”