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# README.markdown

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` There are also any number of hills, each with a fixed position and radius.`
`-These serve as goals; when the leader hedgehog reaches a goal hill, the`
`-troupe's quest is over, and they are free to break formation and nibble on`
`-clover or whatever it is that hedgehogs do for fun.`
`+These serve as goals; when the leader hedgehog reaches a hill, the troupe's`
`+quest is over, and they are free to break formation and nibble on clover or`
`+whatever it is that hedgehogs do for fun.`
` `
` Part IV. Computational Class`
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` real analysis techniques to discover the evolution of the system.  Motion of`
` the hedgehogs would be genuinely continuous except for the points where their`
` velocities change due to one hedgehog approaching another too closely, etc.`
`+`
`+Nor have we said much about the topology of the space all of these things are`
`+in.  Naturally, the space could be infinite, or it could be mapped onto a`
`+torus so that the hedgehogs "wrap around" at the edges.  (The fact that the`
`+space is finite is not a problem w.r.t. Turing-completeness, so long as there`
`+are still an infinite number of possible coordinates, i.e. the space of real`
`+or rational numbers; integers, though, would be problematic in a space of`
`+finite extent.)  Or the space could be mapped onto the surface of a sphere,`
`+with appropriate modifications.`
`+`
`+We have also not constrained the sets of faery rings and hills to be finite;`
`+so we could have an infinite number of them in an infinite space -- but for`
`+correspondence with a Turing machine, these should probably be restricted to`
`+infinite sets.  (Otherwise, if you have, say, an uncountable set of faery`
`+rings, specified non-constructively, you could encode all possible`
`+computations just in them, and the behaviour of the hedgehogs becomes`
`+essentially moot.)`
`+`
`+The initial condition could either consist of the troupe having a leader`
`+hedgehog with an initial velocity, or a leader-elect hedgehog with an`
`+initially-selected faery ring to which it is attracted.  The former is`
`+probably more "natural" for some definition of "natural".`