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The street where I live has been illuminated for the past few weeks by some spectacular Christmas signs in the shape of snowflakes, each composed of a few hundred high-intensity bluish white LEDs.
I'm assuming the LEDs were fitted automatically, using some kind of pick-and-place machine, which is
probably controlled by a computer. It ought to be simple to program this computer to fit some LEDs and omit others, controlled by the output of a LFSR of say 100 bits in length.
For those that don't know, Wikipedia has something to say about LFSRs (link) but the important thing is that they can be used to produce random-looking sequences of ones and zeros that don't repeat themselves for a very long time. A 100 bit LFSR could produce a sequence that won't repeat for 2^100-1 steps, meaning the machine won't repeat its pattern until after it's fitted that many LEDs - which would take it millions of years.
No two snowflakes are alike - guaranteed!
Of course the circuitry will have to be designed to cope with missing LEDs. Driving them in series would result in every snowflake being completely dim.
Guaranteed non-repeating bit sequences [Wrongfellow, Jan 14 2010]
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||Each light could be made with a complete disc of LEDs, and the LFSR routine could run on the controller for the string of lights. That way each time the lights flashed, say once a second, each snowflake on the string would be replaced by a different one. My maths is not up to working out the repeat interval. Nor the number of LEDs required per disc - surely a much smaller limit on the possible number of patterns available?
||That sounds good for the Deluxe model. In addition to this, each unit should be programmed with a distinct feedback polynomial, to maintain the guaranteed non-identicalness.
||You could probably get away with a much smaller hardware LFSR and drive the LEDs directly from the various bits of the shift register - but these days I'm not sure that would be any simpler or cheaper than using an off-the-shelf microcontroller.
||You need extra electronics to filter out the dirty words in
||+ and I like the wording of the description!
||There are rumours that a new society is to be formed: "The Snowflake Spotters Society", whose sole aim in life is to photograph, organise, file and share LED snowflakes in the hope to be the first to verify a duplicate.