Totalistic Cellular Automaton

Author

Eric W. Weisstein
April 15, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/CellularAutomata/TotalisticCellularAutomaton.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/TotalisticCellularAutomaton.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<Graphics`Colors`

Code 777

Show[Graphics[TotalisticCARules[777],AspectRatio->Automatic,PlotRange->All]]

Show[
GraphicsArray[
Table[RasterGraphics[
TotalisticCellularAutomaton[777,20,i],
Mesh->False,
Frame->True,
FrameLabel->None,
FrameTicks->None,
PlotLabel->StyleForm["code "<>ToString[777],FontFamily->"Times",FontSlant->"Italic"]
],{i,2}]
]
]

Code 1083

Show[Graphics[TotalisticCARules[1083],AspectRatio->Automatic]]

Show[
GraphicsArray[
Table[RasterGraphics[
TotalisticCellularAutomaton[1083,20,i],
ColorRules->{0->White,1->RGBColor[.5,.5,.5],2->Black},
Mesh->False,
Frame->True,
FrameLabel->None,
FrameTicks->None,
PlotLabel->StyleForm["code "<>ToString[1083],FontFamily->"Times",FontSlant->"Italic"]
],{i,0,2}]
]
]

Code 1599

Show[Graphics[TotalisticCARules[1599],AspectRatio->Automatic]]

CellularAutomaton[{1599,{3,1}},{{1},0},100]

Show[
RasterGraphics[
CellularAutomaton[{1599,{3,1}},{{1},0},1000],
ColorRules->{0->White,1->RGBColor[.5,.5,.5],2->Black},
PlotLabel->StyleForm["code "<>ToString[1599],FontFamily->"Times",FontSlant->"Italic"]
]
]//Timing

Examples

rules={600,777,993,1020,1074,1083};

Show[GraphicsArray[
{Graphics[{TotalisticCARules[#],Text["code "<>ToString[#],{-4,-1},
TextStyle->{FontFamily->"Times",FontSlant->"Italic"}]},
AspectRatio->Automatic,PlotRange->All]}&/@rules
]
]

Show[GraphicsArray[
Partition[
RasterGraphics[
TotalisticCellularAutomaton[#,25],
ColorRules->{0->White,1->RGBColor[.5,.5,.5],2->Black},
PlotLabel->StyleForm["code "<>ToString[#],FontFamily->"Times",FontSlant->"Italic"]
]&/@rules,2,2,{1,1},{}
]
]
]

Random-Appearing Behavior

rules={177,912,2040};
Show[GraphicsArray[
Partition[
RasterGraphics[
TotalisticCellularAutomaton[#,300],
ColorRules->{0->White,1->RGBColor[.5,.5,.5],2->Black},
PlotLabel->StyleForm["code "<>ToString[#],FontFamily->"Times",FontSlant->"Italic"]
]&/@rules,2,2,{1,1},{}]
]
]

Enumeration

Show/@Table[RasterGraphics[
TotalisticCellularAutomaton[i,20,1],
Mesh->False,
Frame->True,
FrameLabel->None,
FrameTicks->None,
PlotLabel->StyleForm["code "<>ToString[i],FontFamily->"Times",FontSlant->"Italic"]
],{i,100}]