Timeline for Optimizing the layout of Infinite Suburbia
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Jul 20, 2010 at 14:21 | comment | added | Robin Saunders | Here's my concern: I'm sure percolation theory will have much to say about going from a solid, non-traversible packing to an open, traversible one. But once we're restricting ourselves to choosing between the different traversible layouts, is it equipped to talk about optimizing such layouts for a hierarchical system of "streets, roads, highways" etc. where speed is taken into account? | |
| Jul 15, 2010 at 9:42 | comment | added | Tom Boardman | The hexagonal disc packing is the limiting case where we do not care about traversibility at all and the singleton disc embedding is the other limiting case where we do not care about density. My point being that, until we set a weighting, we are probably stuck somewhere arbitrary between these two. But yeah, there may be interesting things we can say without a weighting- and if there are, I'd wager percolation theory would be the language for it. | |
| Jul 15, 2010 at 9:26 | comment | added | Robin Saunders | A plain hexagonal disk packing doesn't work, because there's no empty space for the disks to travel through. You need at least 1/3 of the space to be empty (a straight route can supply access to one row of disks on either side). What I'm wondering is whether something at least fairly close to this density can be attained with better behaviour for E. Even without weighting for the two conditions, investigating how they depend on each other could still prove interesting. Thanks for the link on percolation; this is an area of maths I'd never heard of before! | |
| Jul 15, 2010 at 8:16 | history | answered | Tom Boardman | CC BY-SA 2.5 |