A digital sundial is a clock that indicates the current time with numerals formed by the sunlight striking it. Like a classical
sundial, the device contains no moving parts. It uses no electricity nor other manufactured sources of energy. The digital display changes as the sun advances in its daily course.
Technique
There are two basic types of digital sundials. One type uses
optical waveguides
An optical waveguide is a physical structure that guides electromagnetic waves in the optical spectrum. Common types of optical waveguides include optical fiber waveguides, transparent dielectric waveguides made of plastic and glass, liquid light ...
, while the other is inspired by
fractal geometry.
Optical fiber sundial
Sunlight enters into the device through a slit and moves as the sun advances. The sun's rays shine on ten linearly distributed sockets of optical waveguides that transport the light to a
seven-segment display
A seven-segment display is a form of electronic display device for displaying decimal numerals that is an alternative to the more complex dot matrix displays.
Seven-segment displays are widely used in digital clocks, electronic meters, basic ...
. Each socket fiber is connected to a few segments forming the digit corresponding to the position of the sun.
Fractal sundial
![Digital sundial](https://upload.wikimedia.org/wikipedia/commons/4/4c/Digital_sundial.jpg)
The theoretical basis for the other construction comes from
fractal geometry
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illu ...
. For the sake of simplicity, we describe a two-dimensional (planar) version. Let denote a straight line passing through the origin of a
Cartesian coordinate system and making angle with the -axis. For any define to be the perpendicular projection of on the line .
Theorem
Let , be a family of any sets such that
is a
measurable set
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many simila ...
in the plane. Then there exists a set such that
* ;
* the measure of the set is zero for almost all .
There exists a set with prescribed projections in ''almost'' all directions. This theorem can be generalized to three-dimensional space. For a non-trivial choice of the family , the set described above is a fractal.
Application
Theoretically, it is possible to build a set of masks that produce shadows in the form of digits, such that the display changes as the sun moves. This is the fractal sundial.
The theorem was proved in 1987 by
Kenneth Falconer. Four years later it was described in ''
Scientific American
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it ...
'' by
Ian Stewart. The first prototype of a digital sundial was constructed in 1994; it writes the numbers with light instead of shadow, as Falconer proved. In 1998 a digital sundial was installed for the first time in a public place (
Genk, Belgium). There exist window and tabletop versions as well. Julldozer in October 2015 published an
open-source 3D printed model sundial.
Mojoptix 001: Digital Sundial
/ref>
References
{{Reflist
Sundials