Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Explore the Wireworld Turing-complete cellular automaton
Contributed by: Daniel Sanchez
Wireworld is a Turing-complete cellular automaton first proposed by Brian Silverman in 1987 suited for simulating logic gates and other real-world computer elements.
Installation Instructions
To install this paclet in your Wolfram Language environment,
evaluate this code:
PacletInstall["DanielS/Wireworld"]
To load the code after installation, evaluate this code:
Needs["DanielS`Wireworld`"]
Paclet Guide
Examples
Basic Examples (2)
Evolve a Wireworld state for 2 steps:
| In[1]:= | ![InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 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List[20.928985595703125`, 112.91769218444824`], List[21.882003784179688`, 111.26669120788574`], List[23.428985595703125`, 110.37369346618652`], List[197.5`, 9.87369155883789`], List[198.27300024032593`, 9.426692008972168`], List[199.13700008392334`, 9.203690528869629`], List[200.`, 9.203690528869629`], List[200.86299991607666`, 9.203690528869629`], List[201.72699999809265`, 9.426692008972168`], List[202.5`, 9.87369155883789`], List[376.5710144042969`, 110.37369346618652`], List[378.1179962158203`, 111.26669120788574`], List[379.0710144042969`, 112.91769218444824`], List[379.0710144042969`, 114.70369529724121`], List[379.0710144042969`, 315.7036876678467`], List[379.0710144042969`, 317.4896984100342`], List[378.1179962158203`, 319.1406993865967`], List[376.5710144042969`, 320.03370475769043`]]]]], List[FaceForm[List[RGBColor[0.5529411764705883`, 0.6745098039215687`, 0.8117647058823529`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 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"Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["DanielS/Wireworld", "DanielS`Wireworld`WireworldEvolve"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][SparseArray[
Automatic, {5, 11}, 0, {1, {{0, 0, 2, 12, 14, 14}, {{5}, {6}, {1}, {2}, {3}, {4}, {5}, {
7}, {8}, {9}, {10}, {11}, {5}, {6}}}, {3, 3, 3, 3, 2, 1, 3, 3, 3, 2, 1, 3, 3, 3}}], 2]](https://www.wolframcloud.com/obj/resourcesystem/images/359/3591cb51-8d6c-4be5-a8c5-d726e9e46e94/1-0-6/632db328b306514a.png) |
| Out[1]= |  |
Plot a Wireworld state:
| In[2]:= | ![InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 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"Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["DanielS/Wireworld", "DanielS`Wireworld`WireworldPlot"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][SparseArray[
Automatic, {13, 24}, 0, {1, {{0, 0, 0, 8, 15, 24, 28, 34, 38, 47, 54, 62, 62, 62}, {{
4}, {5}, {6}, {7}, {8}, {9}, {10}, {11}, {3}, {12}, {13}, {14}, {
15}, {16}, {17}, {4}, {5}, {6}, {7}, {8}, {9}, {10}, {11}, {18}, {
17}, {18}, {19}, {20}, {17}, {20}, {21}, {22}, {23}, {24}, {17}, {
18}, {19}, {20}, {4}, {5}, {6}, {7}, {8}, {9}, {10}, {11}, {18}, {
3}, {12}, {13}, {14}, {15}, {16}, {17}, {4}, {5}, {6}, {7}, {8}, {
9}, {10}, {11}}}, {3, 3, 3, 3, 3, 3, 2, 1, 3, 3, 3, 3, 3, 2, 1, 3,
3, 3, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 3, 3, 3, 3, 3, 2, 1, 3, 3, 3, 3, 2, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3}}]]](https://www.wolframcloud.com/obj/resourcesystem/images/359/3591cb51-8d6c-4be5-a8c5-d726e9e46e94/1-0-6/444eb3974d861dd2.png) |
| Out[2]= |  |
Scope (2)
Test whether a matrix is a valid Wireworld state:
| In[3]:= | ![InterpretationBox[FrameBox[TagBox[TooltipBox[PaneBox[GridBox[List[List[GraphicsBox[List[Thickness[0.0025`], List[FaceForm[List[RGBColor[0.9607843137254902`, 0.5058823529411764`, 0.19607843137254902`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]], List[List[0, 2, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3], List[0, 1, 0], List[1, 3, 3]]], List[List[List[205.`, 22.863691329956055`], List[205.`, 212.31669425964355`], List[246.01799774169922`, 235.99870109558105`], List[369.0710144042969`, 307.0436840057373`], List[369.0710144042969`, 117.59068870544434`], List[205.`, 22.863691329956055`]], List[List[30.928985595703125`, 307.0436840057373`], List[153.98200225830078`, 235.99870109558105`], List[195.`, 212.31669425964355`], List[195.`, 22.863691329956055`], List[30.928985595703125`, 117.59068870544434`], List[30.928985595703125`, 307.0436840057373`]], List[List[200.`, 410.42970085144043`], List[364.0710144042969`, 315.7036876678467`], List[241.01799774169922`, 244.65868949890137`], List[200.`, 220.97669792175293`], List[158.98200225830078`, 244.65868949890137`], List[35.928985595703125`, 315.7036876678467`], List[200.`, 410.42970085144043`]], List[List[376.5710144042969`, 320.03370475769043`], List[202.5`, 420.53370475769043`], List[200.95300006866455`, 421.42667961120605`], List[199.04699993133545`, 421.42667961120605`], List[197.5`, 420.53370475769043`], List[23.428985595703125`, 320.03370475769043`], List[21.882003784179688`, 319.1406993865967`], List[20.928985595703125`, 317.4896984100342`], List[20.928985595703125`, 315.7036876678467`], List[20.928985595703125`, 114.70369529724121`], 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0]]], List[List[List[44.92900085449219`, 282.59088134765625`], List[181.00001525878906`, 204.0298843383789`], List[181.00001525878906`, 46.90887451171875`], List[44.92900085449219`, 125.46986389160156`], List[44.92900085449219`, 282.59088134765625`]]]]], List[FaceForm[List[RGBColor[0.6627450980392157`, 0.803921568627451`, 0.5686274509803921`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[355.0710144042969`, 282.59088134765625`], List[355.0710144042969`, 125.46986389160156`], List[219.`, 46.90887451171875`], List[219.`, 204.0298843383789`], List[355.0710144042969`, 282.59088134765625`]]]]], List[FaceForm[List[RGBColor[0.6901960784313725`, 0.5882352941176471`, 0.8117647058823529`], Opacity[1.`]]], FilledCurveBox[List[List[List[0, 2, 0], List[0, 1, 0], List[0, 1, 0], List[0, 1, 0]]], List[List[List[200.`, 394.0606994628906`], List[336.0710144042969`, 315.4997024536133`], List[200.`, 236.93968200683594`], List[63.928985595703125`, 315.4997024536133`], List[200.`, 394.0606994628906`]]]]]], List[Rule[BaselinePosition, Scaled[0.15`]], Rule[ImageSize, 10], Rule[ImageSize, 15]]], StyleBox[RowBox[List["WireworldStateQ", " "]], Rule[ShowAutoStyles, False], Rule[ShowStringCharacters, False], Rule[FontSize, Times[0.9`, Inherited]], Rule[FontColor, GrayLevel[0.1`]]]]], Rule[GridBoxSpacings, List[Rule["Columns", List[List[0.25`]]]]]], Rule[Alignment, List[Left, Baseline]], Rule[BaselinePosition, Baseline], Rule[FrameMargins, List[List[3, 0], List[0, 0]]], Rule[BaseStyle, List[Rule[LineSpacing, List[0, 0]], Rule[LineBreakWithin, False]]]], RowBox[List["PacletSymbol", "[", RowBox[List["\"DanielS/Wireworld\"", ",", "\"DanielS`Wireworld`WireworldStateQ\""]], "]"]], Rule[TooltipStyle, List[Rule[ShowAutoStyles, True], Rule[ShowStringCharacters, True]]]], Function[Annotation[Slot[1], Style[Defer[PacletSymbol["DanielS/Wireworld", "DanielS`Wireworld`WireworldStateQ"]], Rule[ShowStringCharacters, True]], "Tooltip"]]], Rule[Background, RGBColor[0.968`, 0.976`, 0.984`]], Rule[BaselinePosition, Baseline], Rule[DefaultBaseStyle, List[]], Rule[FrameMargins, List[List[0, 0], List[1, 1]]], Rule[FrameStyle, RGBColor[0.831`, 0.847`, 0.85`]], Rule[RoundingRadius, 4]], PacletSymbol["DanielS/Wireworld", "DanielS`Wireworld`WireworldStateQ"], Rule[Selectable, False], Rule[SelectWithContents, True], Rule[BoxID, "PacletSymbolBox"]][SparseArray[
Automatic, {3, 10}, 0, {1, {{0, 5, 10, 15}, {{6}, {7}, {8}, {9}, {10}, {1}, {2}, {3}, {
4}, {5}, {6}, {7}, {8}, {9}, {10}}}, {1, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 3, 3, 3, 3}}]]](https://www.wolframcloud.com/obj/resourcesystem/images/359/3591cb51-8d6c-4be5-a8c5-d726e9e46e94/1-0-6/11a36163d8589ef5.png) |
| Out[3]= |  |
Open a window and draw/edit a Wireworld state:
Interactive Examples (2)
Animate the evolution of an OR gate fed by two electron sources:
| In[4]:= | ![(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/71d7c70d-dfde-4a23-b9a4-1675e17cb882"]](https://www.wolframcloud.com/obj/resourcesystem/images/359/3591cb51-8d6c-4be5-a8c5-d726e9e46e94/1-0-6/0cf238d29776d42f.png) |
| Out[4]= |  |
Animate the behaviour of an OR gate, an XOR gate and an inverter:
| In[5]:= | ![(* Evaluate this cell to get the example input *) CloudGet["https://www.wolframcloud.com/obj/fde41fdb-c8e5-4a51-a79b-822773582e64"]](https://www.wolframcloud.com/obj/resourcesystem/images/359/3591cb51-8d6c-4be5-a8c5-d726e9e46e94/1-0-6/2c55fa043f537277.png) |
| Out[5]= |  |
Publisher
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Wolfram Language Version 13.0
External Links
- https://www.quinapalus.com/wi-index.html
- Wireworld - Wikipedia
- https://mathworld.wolfram.com/WireWorld.html
- Note (b) for Class 4 Behavior and Universality: A New Kind of Science | Online by Stephen Wolfram[Page 1117]
- World Wide WireWorld