Digital sundial

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.

There are two basic types of digital sundials. One type uses optical waveguides, while the other is inspired by fractal geometry.

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. Each socket fiber is connected to a few segments forming the digit corresponding to the position of the sun.

The theoretical basis for the other construction comes from fractal geometry. For the sake of simplicity, we describe a two-dimensional (planar) version. Let L_θ denote a straight line passing through the origin of a Cartesian coordinate system and making angle θ ∈ [0,π) with the x-axis. For any F ⊂ ℝ² define proj_θF to be the perpendicular projection of F on the line L_θ.

Let G_θ ⊂ L_θ, θ ∈ [0,π) be a family of any sets such that ${\displaystyle \bigcup _{\theta }}$ G_θ is a measurable set in the plane. Then there exists a set F ⊂ ℝ² such that

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