I'll start by describing the units from which this machine would be built.
There is a cube about a fifth of a millimetre on a side. Its surfaces are touch-sensitive and can change colour corresponding to the RGB value of an unsigned three-byte integer stored within it. This value is read-write. The cube also stores a thirty-two bit number used to identify itself and a separate three-byte number, both initially read-only but which can be set to read-write. It also contains a rechargeable battery, a photocell, a CPU, and a radio receiver and transmitter. It can be charged by induction and communicates with other units like it using radio signals. It is also waterproof.
On receiving a special "reset" signal, each unit attempts to find other units nearby. They then count each other and transmit and receive their identifying values, looking for values which differ from their own identifiers by one. If they find none, they increment or decrement their values to the closest identifier which can be found. This enables them to allocate themselves as a block of RAM. They then find the largest block of ascending identifiers and look for a unique twenty-four bit number which indicates the start of system software, check that it's long enough to contain all of it, and start to execute it. This begins the boot process.
Photocells enable the units to identify themselves as visible or invisible to the outside world. Receivers and transmitters mean the units can communicate with each other for processing purposes or, in concert, form a wireless link with a network or peripherals.
The units are generally set inside a water-soluble adhesive matrix, and there are up to around four billion of them. They organise themselves as a computer whose storage and processing capabilities depends on how many of them there are, which they can count. One configuration is as a large cuboidal slab, like a tablet PC. This computer (clearly its architecture is not like that of a PC in the contemporary sense of the word) is able to display anywhere on its surface, store data in the read-only state of the storage if set, is touch-sensitive, can interact with a network and wireless devices, has a camera capability, particularly if a drop of water or other lens is placed somewhere on its surface, and could probably pick up sounds. It would be able to produce sound via radio transmission.
Also, it can be "dissolved" in water. On being placed in water, it disintegrates as the adhesive goes into solution. The computer solution can then be separated into a number of smaller parts and recrystallised by evaporation to form smaller devices with lower specifications. It can also be broken into parts and continue to function in the same way, and be formed into different shapes, painted on surfaces and so forth.
I imagine it working in a similar way to cellular automata.-- nineteenthly, Jan 24 2012 Modular neural network shameless self promotion [xaviergisz, Jan 24 2012] I really like the idea of a self-organising set of "smart-dust" (see link later) and think it's all 'doable' with the exception of the bit you missed out which was to allow them to 'crystallise' or to form themselves into any kind of recognisable shape. Which may not be necessary, maybe you could just get out a rolling-pin and spread-out a glob of these things on a worksurface and prop it up to watch tv.
But most of all, I'd be worried about people accidentally washing too many smart particles down the sink and ending up with a supercomputer emerging from the sewers! It'd be a great plotline for a story.-- zen_tom, Jan 24 2012 I like this. I'm not sure what it would be good at/for, but I like it.-- MaxwellBuchanan, Jan 24 2012 A thought on the crystallization process. Magnets are always good and, if a pattern of north/south poles could be arranged to appear on each face, then these things would self-assemble into cubical arrays.
Actually hang on, I might post that...-- MaxwellBuchanan, Jan 24 2012 I think the most difficult bit would be the architecture- if you're dissolving it like this, you have to be able to build a coherent operating system via a random assortment of three-byte numbers, arranged with random interconnects and random dispersal throughout the memory space.
I can think of a few solutions, but they all require either special modules, extremely controlled starting conditions in terms of module mixes, or outside equipment to put the tablet together.
You also have the problem of losing all non-backed- up files if you compute in a damp room.-- Hive_Mind, Jan 29 2012 If it's running a bit slowly, could you add FLOPS by the teaspoon-full?-- mouseposture, Jan 29 2012 random, halfbakery