Cellular automaton machine

[aeh5040]

Here is my latest endeavour in mechanical computation.  Cellular automata are among the simplest possible computers.  One of the most famous is Conway's Game of Life which runs on a two-dimensional array of cells, but even cellular automata on one-dimensional universes can be interesting, and some, such as rule 110 are known to be Turing complete (i.e. can do arbitrary computation).  As is my wont, I wanted to see if I could implement one of these entirely mechanically.  The device implements a version of the XOR rule (or rule 60), an even simpler cellular automaton that produces fractal space-time histories.

There are 8 units, each of which can be in the "up" or "down" state. They are scanned cyclically in clockwise order (via the chain drive). When a unit is scanned, if is in the up state then the state of the previous unit is toggled (changed to the opposite state). The pattern repeats every 8x8x7=448 steps (8x7=56 revolutions). Every 56 steps, all units are up, and then all but one are switched to down in succession.

So far the device is 100% reliable!

 

Edited December 27, 2017 by aeh5040

[Limga]

That is amazing.
I am still have to work out how this cellular automaton machine works, but I understand that cellular automatons are not the easiest things to build from LEGO pieces. Nice work!

[mocbuild101]

Very interesting... But I can't really understand how the chain can make them move in that pattern... Could you show more of the internal mechanisms?

[aeh5040]

Just now, mocbuild101 said:

Very interesting... But I can't really understand how the chain can make them move in that pattern... Could you show more of the internal mechanisms?

Most important parts of the mechanism are actually visible in the video, although I understand it's hard to see what is happening! 

The chain contains four wide track links, and the rest is normal chain.  When those four pass the knob wheels at the top of a unit, they rotate the central vertical axle by one turn.  The central axle has a driving ring (the new 3L type on the smooth Porsche axle connector), so that depending on the position of a changeover catch the central axle it is connected either to nothing or (via a 1:2 gear ratio) to a crank (Bionical weapon barrel) on the _previous_ unit in the circle.  That crank controls the changeover catch of that unit - a half turn toggles the changeover catch to the opposite position.  Apart from the gearing (which isn't important except that it is a 1:2 ratio), the only thing not clearly visible is a detent mechanism, which ensures that the crank snaps cleanly into one of two positions 180 degrees apart.  (That is essential, otherwise errors would quickly accumulate).

[Aventador2004]

Very interesting, head bending engineering 

[BusterHaus]

Fantastic work! I'm guessing this is a modular machine that can have as many cells/units as you want? 

[Jurss]

Amazing!

[Boulderer]

Love it 

[JopieK]

Very nice work aeh5040! Could you also implement other operations?

[LucyCol]

As a certain Mr Spock used to say 'Fascinating' 

[kieran]

Nice one. Is fun to watch 

[aeh5040]

Thank you for the nice comments folks.  (I was a bit worried it would be too esoteric for anyone to appreciate!)

19 hours ago, BusterHaus said:

Fantastic work! I'm guessing this is a modular machine that can have as many cells/units as you want? 

Yes, exactly.  You can hook up as many of the units as you want in a ring (or just in a line).  The only thing that would need to change is the geometry of the physical bracing and the chain drive.  Currently 135 degree angle connectors are used to get the 8-fold symmetry.  Interestingly, if the number of units is not a power of two, it would typically take MUCH longer for the pattern to repeat.  E.g. with 10 units I think it takes 8890 steps.

14 hours ago, JopieK said:

Very nice work aeh5040! Could you also implement other operations?

No reason why not in principle, although it would be harder.  Perhaps differentials could be used.  Of course, a Turing complete rule would be good!

One thing I would like to improve is to replace the yellow "flags" with something larger and more visible (that moves or changes color).  The issue is theat it needs to take very little force to activate it.  Any ideas welcome...