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Cat's Eye Technologies
10 years ago

99 | 99 | --------------- |

100 | 100 | |

101 | 101 | There are also any number of hills, each with a fixed position and radius. |

102 | These serve as goals; when the leader hedgehog reaches a goal hill, the | |

103 | troupe's quest is over, and they are free to break formation and nibble on | |

104 | clover or whatever it is that hedgehogs do for fun. | |

102 | These serve as goals; when the leader hedgehog reaches a hill, the troupe's | |

103 | quest is over, and they are free to break formation and nibble on clover or | |

104 | whatever it is that hedgehogs do for fun. | |

105 | 105 | |

106 | 106 | Part IV. Computational Class |

107 | 107 | ---------------------------- |

194 | 194 | real analysis techniques to discover the evolution of the system. Motion of |

195 | 195 | the hedgehogs would be genuinely continuous except for the points where their |

196 | 196 | velocities change due to one hedgehog approaching another too closely, etc. |

197 | ||

198 | Nor have we said much about the topology of the space all of these things are | |

199 | in. Naturally, the space could be infinite, or it could be mapped onto a | |

200 | torus so that the hedgehogs "wrap around" at the edges. (The fact that the | |

201 | space is finite is not a problem w.r.t. Turing-completeness, so long as there | |

202 | are still an infinite number of possible coordinates, i.e. the space of real | |

203 | or rational numbers; integers, though, would be problematic in a space of | |

204 | finite extent.) Or the space could be mapped onto the surface of a sphere, | |

205 | with appropriate modifications. | |

206 | ||

207 | We have also not constrained the sets of faery rings and hills to be finite; | |

208 | so we could have an infinite number of them in an infinite space -- but for | |

209 | correspondence with a Turing machine, these should probably be restricted to | |

210 | infinite sets. (Otherwise, if you have, say, an uncountable set of faery | |

211 | rings, specified non-constructively, you could encode all possible | |

212 | computations just in them, and the behaviour of the hedgehogs becomes | |

213 | essentially moot.) | |

214 | ||

215 | The initial condition could either consist of the troupe having a leader | |

216 | hedgehog with an initial velocity, or a leader-elect hedgehog with an | |

217 | initially-selected faery ring to which it is attracted. The former is | |

218 | probably more "natural" for some definition of "natural". |