Re: Trouble Implementing Schelling's Segregation Model
- To: mathgroup at smc.vnet.net
- Subject: [mg91676] Re: Trouble Implementing Schelling's Segregation Model
- From: Steve_Kinsella <stephen.kinsella at gmail.com>
- Date: Thu, 4 Sep 2008 06:39:00 -0400 (EDT)
- References: <g7uo2p$5un$1@smc.vnet.net>
Anybody?
Steve_Kinsella wrote:
> Hi All,
>
> I'm trying to write a demonstration for a class on Schelling's 1978
> segregation model. An implementation exists from Gaylord and D'Andria,
> 1998, but it's not playing ball with Mathematica 6.0. If anyone wants
> to take a pop at the code below, I'd appreciate it. Thanks, Steve
>
> (*Schelling Model (1978, 147 - 153) Demonstration
>
> Model uses a square n*n lattice with wraparound boundary conditions \
> with a population density p of individuals occupying lattice sites \
> and the rest empty. System evolves over t time steps. *)
>
> neighborhood[n_, p_, v_, w_, t_] :=
> Module[{walk, movestay, society, RND, Moore, GN} ,
> RND := RandomInteger[ {1, 4}]
> society :=
> Table[Floor[p + RandomInteger[]], {n}, {n}] /.
>
> 1 :> {RND, Table[Integer, {1, w}], {v}};
> movestay[0, __] := 0;
> movestay[{a_, b_},
> res__] := {a*
> Round[1 -
> Count[Map[
> Count[b - #[[2]], 0] &, {res}/.0 -> {0,
> 0}], _?{# >= v/2 &}]/8.] , b };
> (*Walk Rules*)
>
> Moore[func_, lat_] :=
> MapThread[func,
> Map[RotateRight[lat, #] &, {{0, 0}, {1, 0}, {0, -1}, {-1, 0}, {0,
> 1}, {1, -1}, {-1, -1}, {-1, 1}, {1, 1}} , 2];
> GN[func_, lat_] :=
> MapThread[func,
> Map[RotateRight[lat, #] &, {{0, 0}, {1, 0}, {0, -1}, {-1,
> 0}, {0, 1}, {1, -1}, {-1, -1}, {-1, 1}, {1, 1}, {2,
> 0}, {0, -2}, {-2, 0}, {0, 2}}], 2];
> NestList[GN[walk, Moore[movestay, #]] &, society, t]]]
>
> SeedRandom[9]
> results = neighborhood[20, 0.6, 1, 2, 500]
>
> Show[GraphicsArray[
> Map[Show[Graphics[
> Raster[# /. {0 -> RGBColor[0.7, 0.7, 0.7], {_, {1}} ->
> RGBColor[0, 1, 0], {_, {2}} -> RGBColor[0, 0, 1]}]],
> AspectRatio -> Automatic, DisplayFunction -> Identity] &, {First[
> results], Last[results]}]]]