h a l f b a k e r y
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To illustrate the idea with a hydraulic analogy, imagine one needs to solve an extremely complex maze. An ultraviolet image of the maze is projected onto a sheet of metal coated with UV-sensitive plastic. The UV-affected plastic is removed, then the metal is etched to a depth of few millimeters. The
sheet is then covered with a stiff sheet of clear plastic, which is glued in place. Now two small holes are made: one at the start of the maze and one at its exit.
One can now solve the maze by pumping colored fluid (or smoke) through the hole at the starting point. The fluid will follow the correct path without even having to "think". It will of course drift into other paths, but hopefully not before you've noted the correct path. You might want to prefill the entire maze with clear or white fluid before this step to improve contrast and reduce drifting into other paths.
A more practical approach would involve replacing the hydraulic solver with its equivalent electronic circuit.
One could for example, project the maze onto a sheet of photo-conductive material and thereby form a conductive path from the start to the exit of the maze. A voltage would then be applied across the start and end points. The resulting current would instantly "solve" the maze. The question is, how to "read" the solution?
For the greatest possible flexibility, it would be better to create a large array of digitally controlled resistors, connected four or more to a node. After setting the values of the resistors to model a problem, a voltage is applied between the start and end points. At each node, the voltage drops across all resistors connected to it are compared and the path (resistor) with the lowest drop is followed to its other node. This pattern is followed until the end point is reached.
To improve reading of the results, it might be helpful if each resistor had settings to bypass it or disconnect it from the array without changing its resistance value. This feature would be used during the reading of a solution to maximize the differences in voltages at other nodes.
With the increasing advances in printable circuitry, it might be feasible to print patterns as large as a (8.5" x 11") sheet of paper on plastic film (for extra smoothness). This would avoid the need for arrays of digital resistors.
One application might be planning routes in large cities.
This reminds me...
...that soap films can be used to plan road networks. [Wrongfellow, Dec 02 2011]
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||[+] for a nifty way of solving mazes.
||+ just for being interesting, and for the maze solution.
||I like this. Not because it's analog computers, but
because of the possibility of using a digital computer
to make a disposable analog machine to solve a
||So, what you are proposing is a sort of FPGA, but
with analog components instead of digital ones?
Instead of a programmable network of logic gates
and suchlike, you'd have a programmable network
of variable resistors, capacitors, inductors, and
||If instead you're proposing a set of 3d printing
devices for various analog-mechanical problem
solvers, that's also cool. Perhaps there's also a
chamber in which a maze is constructed, carefully
placed sweetened oat flakes are set down, and
slime molds are dumped.
The above example might be useful considering the layouts of some cities, but it was mainly to illustrate the general idea of using unconventional "logic" devices to solve hard problems quickly. By combining "logic" forms in imaginative ways, one might be able to solve a wide range of problem types more quickly.
As another example, one might try to perform real-time antialiasing with a CRT monitor having a second set of weaker beams that diverge so that they strike the eight pixels surrounding the current one. A graphics card designed to support such a monitor would control which regions are antialiased so one isn't forced to have either all or none at all.
||[+] No m-f-d call, but reminiscent of the economy simulator in the basement of the Royal Morporkian Bank.