I have recently re-discovered the digital sundial, which is essentially based on the idea that a fractal 3D object can cast a different shadow at each moment of the day (as explained in this book from K. J. Falconer [1]).
And I was wondering if something like this could be used to boil some wather (to produce electricity on a small scale): imagine a mirror that reflects and focuses
the light of the sun on the same point for the whole day!
So I started looking for websites about fractals, optics and lenses...
But there was apparently nothing useful: the articles and discussions where either too complex and theoretical or unrelated (for example there are plenty websites about fractals using the word "mirror"...)
Finally I stumbled upon the concept of "sun cooking"...
It seems that you can boil wather (for cooking) with very little human intervention using a parabolic mirror, that in turn can be built with very cheap materials, eventually even cartboard and aluminium!!
(The nice website even provides plans to build your own sun cooker!)
However, I'm still considering how one can build a composite mirror (a mirror made of smaller mirrors) that could project sun rays in more or less the same point for the whole day.
(Perhaps I should try and use some math to design a small prototype...)
[1] K. J. Falconer. Sets with prescribed projections and Nikodym sets. Proc. London Math. Soc. (3) 53 (1986), no. 1, 48-64.
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