Re: Trouble Implementing Schelling's Segregation Model

• To: mathgroup at smc.vnet.net
• Subject: [mg91684] Re: Trouble Implementing Schelling's Segregation Model
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Fri, 5 Sep 2008 07:13:02 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <g7uo2p\$5un\$1@smc.vnet.net>

```Steve_Kinsella wrote:

> 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

It would have been better if you told us what issues you encountered
with the code below. I have corrected two potential syntax/semantic errors.

> (*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}};

You must add a ";" semi-column after RandomInteger[], otherwise
Mathematica will interpret the space as an implicit multiplication with
society.

>   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_] :=
>     Map[RotateRight[lat, #] &, {{0, 0}, {1, 0}, {0, -1}, {-1, 0}, {0,
>        1}, {1, -1}, {-1, -1}, {-1, 1}, {1, 1}} , 2];

It seems that a square bracket is missing to end the MapThread[] function.

>     GN[func_, lat_] :=
>       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]}]]]

So your code could be as follows (note that it is still not working, but
for other reasons that syntactic ones).

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[(Count[b - #1[[2]], 0] & ) /@ ({res}/0. ->
{0, 0}), _?({#1 >= v/2 & })]/8.], b};

Map[RotateRight[lat, #1] & , {{0, 0}, {1, 0}, {0, -1}, {-1, 0},
{0, 1}, {1, -1}, {-1, -1}, {-1, 1}, {1, 1}}, 2]];

(RotateRight[lat, #1] & ) /@ {{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, #1]] & , society, t]]

SeedRandom[9]
results = neighborhood[20, 0.6, 1, 2, 500]
Show[GraphicsArray[
(Show[Graphics[Raster[#1 /. {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]}]]

Hope this helps,
-- Jean-Marc

```

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