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Catastrophes in Complex Systems
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Simulating Experiences:
Excursions in Programming
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Mathematica code as it appeared in Mathematica in Education,
Volume 2 Number 1, Fall 1992
;[s]
4:0,0;11,1;35,2;61,3;90,-1;
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Richard J. Gaylord
Department of Materials Science
University of Illinois, Champaign
Champaign, IL 61801
gaylord@ux1.cso.uiuc.edu
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% End of Graphics
MathPictureEnd
:[font = section; inactive; Cclosed; preserveAspect; startGroup; ]
Color catastrophe (GraphicsArray)
:[font = input; preserveAspect; ]
catastropheG[s_Integer] := Module[{},
initconfig = Table[Random[Integer,{0,3}], {s},{s}];
initconfig[[Random[Integer,{1,s}],Random[Integer,{1,s}]]] = 4;
absorbingBC =
(Prepend[Append[Map[Prepend[Append[#,0],0]&,#],
Table[0,{Length[#]+2}]],Table[0,{Length[#]+2}]])&;
topples = (Map[(If[#>3,#-4,#])&,#,{2}])&;
nbHgts = (Count[Flatten[#][[{2,4,6,8}]],4|5|6|7])&;
increments = (Map[nbHgts,Partition[absorbingBC[#],{3,3},{1,1}],{2}])&;
frames = FixedPointList[(topples[#]+increments[#])&,initconfig];
p1 = Table[
BarChart3D[frames[[j]],PlotRange->{{0,s+1},{0,s+1},{0,7}},
DisplayFunction->Identity],
{j,1,6}];
Show[GraphicsArray[Partition[p1,3]]]
];
:[font = input; preserveAspect; ]
SeedRandom[1]
:[font = input; preserveAspect; startGroup; ]
catastropheG[8]
:[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 206; ]
%!
%%Creator: Mathematica
%%AspectRatio: .73242
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%% Graphics
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% Scaling calculations
0.02381 0.952381 0.017439 0.952381 [
[ 0 0 0 0 ]
[ 1 .73242 0 0 ]
] MathScale
% Start of Graphics
1 setlinecap
1 setlinejoin
newpath
[ ] 0 setdash
0 g
p
P
0 0 m
1 0 L
1 .73242 L
0 .73242 L
closepath
clip
newpath
p
p
% Start of sub-graphic
p
.02381 .41736 .32143 .71498 MathSubStart
%% Graphics3D
/Courier findfont 8 scalefont setfont
% Scaling calculations
-0.026052 1.101837 0.027546 1.101837 [
[(0)] .10149 .24974 .98066 1 Msboxa
[(2)] .21387 .20226 .89911 1 Msboxa
[(4)] .33202 .15236 .81757 1 Msboxa
[(6)] .4564 .09987 .73603 1 Msboxa
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The Unformatted text for this cell was not generated.
Use options in the Actions Preferences dialog box to
control when Unformatted text is generated.
;[o]
-GraphicsArray-
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ListDensityPlot catastrophe (animation)
:[font = input; preserveAspect; ]
catastropheD[s_Integer] := Module[{},
initconfig = Table[Random[Integer,{0,3}], {s},{s}];
initconfig[[Random[Integer,{1,s}],Random[Integer,{1,s}]]] = 4;
absorbingBC =
(Prepend[Append[Map[Prepend[Append[#,0],0]&,#],
Table[0,{Length[#]+2}]],Table[0,{Length[#]+2}]])&;
topples = (Map[(If[#>3,#-4,#])&,#,{2}])&;
nbHgts = (Count[Flatten[#][[{2,4,6,8}]],4|5|6|7])&;
increments = (Map[nbHgts,Partition[absorbingBC[#],{3,3},{1,1}],{2}])&;
frames = FixedPointList[(topples[#]+increments[#])&,initconfig];
Map[(ListDensityPlot[7 - frames[[#]] ])&,
Range[Length[frames]]]
];
:[font = input; preserveAspect; startGroup; ]
catastropheD[16]
:[font = postscript; PostScript; formatAsPostScript; output; inactive; Cclosed; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 282; startGroup; ]
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ListDensityPlot catastrophe (GraphicsArray)
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catastropheDGG[s_Integer] := Module[{},
initconfig = Table[Random[Integer,{0,3}], {s},{s}];
initconfig[[Random[Integer,{1,s}],Random[Integer,{1,s}]]] = 4;
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topples = (Map[(If[#>3,#-4,#])&,#,{2}])&;
nbHgts = (Count[Flatten[#][[{2,4,6,8}]],4|5|6|7])&;
increments = (Map[nbHgts,Partition[absorbingBC[#],{3,3},{1,1}],{2}])&;
frames = FixedPointList[(topples[#]+increments[#])&,initconfig];
p2 = Table[ListDensityPlot[7-frames[[j]],DisplayFunction->Identity],
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Show[GraphicsArray[ Partition[p2,3] ]]
]
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catastropheDGG[16]
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.0015 w
.74038 .01923 m
.74038 .98077 L
s
P
p
[ ] 0 setdash
.0015 w
.80048 .01923 m
.80048 .98077 L
s
P
p
[ ] 0 setdash
.0015 w
.86058 .01923 m
.86058 .98077 L
s
P
p
[ ] 0 setdash
.0015 w
.92067 .01923 m
.92067 .98077 L
s
P
p
[ ] 0 setdash
.0015 w
.98077 .01923 m
.98077 .98077 L
s
P
p
[ ] 0 setdash
.0015 w
.01923 .0