Re: Trouble Implementing Schelling's Segregation Model
- To: mathgroup at smc.vnet.net
- Subject: [mg91759] Re: Trouble Implementing Schelling's Segregation Model
- From: "Stephen Kinsella" <stephen.kinsella at gmail.com>
- Date: Sun, 7 Sep 2008 05:37:26 -0400 (EDT)
- References: <g7uo2p$5un$1@smc.vnet.net> <48C0EFF2.1030802@gmail.com>
Jean-Marc,
Thanks for your time, I really appreciate it.
Best,
Stephen
On Fri, Sep 5, 2008 at 9:38 AM, Jean-Marc Gulliet <
jeanmarc.gulliet at gmail.com> wrote:
> 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_] :=
>> MapThread[func,
>> 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_] :=
>> 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]}]]]
>>
>
> 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};
>
> Moore[func_, lat_] := MapThread[func,
>
> Map[RotateRight[lat, #1] & , {{0, 0}, {1, 0}, {0, -1}, {-1, 0},
> {0, 1}, {1, -1}, {-1, -1}, {-1, 1}, {1, 1}}, 2]];
>
> GN[func_, lat_] := MapThread[func,
> (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
>
--
Dr. Stephen Kinsella
www.stephenkinsella.net