Závěrečná všehochuť

Antonín Slavík
Matematicko-fyzikální fakulta UK

Práce s jednotkami

Reprezentace veličin s jednotkami:

?Quantity

Quantity[12,"Meters"]

g=Quantity[9.81,"Meters"/"Seconds"^2]

QuantityUnit[g]

QuantityMagnitude[g]

Free-form input (interpretace pomocí Wolfram Alpha):

Quantity["80 km/h"]

InputForm[%]

Quantity["20 fahrenheits"]//InputForm

Převody jednotek:

?UnitConvert

UnitConvert[Quantity[8.2,"Miles"],"Kilometers"]

UnitConvert[Quantity[20,"DegreesCelsius"]]

Zjednodušování jednotek:

UnitSimplify[Quantity[2,("Grams"*"Meters"^2)/"Seconds"^3]]

UnitSimplify[Quantity[2,("Kilograms"^2"Meters")/("Amperes"^2"Seconds"^6)]]

Počítání s jednotkami:

Quantity[2,"Inches"]+Quantity[10,"Centimeters"]

v=Quantity[100,"Kilometers"]/Quantity[60,"Minutes"]

Mnoho funkcí v Mathematice umí pracovat s jednotkami:

Solve[Quantity[m,"Meters"]==Quantity[y,"Yards"],m]

Integrate[Quantity[9.81,"Meters"/"Seconds"^2]*t,{t,Quantity[0,"Seconds"],Quantity[10,"Seconds"]}]

s1=Quantity[RandomReal[{0,1},5],"Meters"]

s2=Quantity[RandomReal[{0,100},5],"Centimeters"]

s=Join[s1,s2]

{Min[s],Max[s],Mean[s]}

Sort[s]

units={"Centimeters","Inches","Feet","Yards","Meters"};
values=Map[Quantity,units]

BarChart[values,ChartLegends->units,BarOrigin->Left,ChartStyle->"Rainbow",AxesLabel->Automatic]

Údaje z integrovaných databází jsou doplněny jednotkami:

teploty=WeatherData["Prague","Temperature",{2022,1,1},"Value"]

ListLinePlot[teploty,AxesLabel->Automatic]

ListLinePlot[teploty,AxesLabel->Automatic,TargetUnits->"Fahrenheit"]

Pravděpodobnost, statistika

Diskrétní rozdělení pravděpodobnosti – příklady:

Rovnoměrné rozdělení DiscreteUniformDistribution[{(Subscript[i, min]),(Subscript[i, max])}]

Binomické rozdělení BinomialDistribution[n,p]

Geometrické rozdělení GeometricDistribution[p]

Poissonovo rozdělení PoissonDistribution[μ]

Spojitá rozdělení – příklady:

Rovnoměrné rozdělení UniformDistribution[{min,max}]

Normální rozdělení NormalDistribution[μ,σ]

(χ^2) rozdělení ChiSquareDistribution[ν]

Studentovo rozdělení StudentTDistribution[ν]

Střední hodnota, rozptyl:

Mean[BinomialDistribution[n,p]]

Variance[BinomialDistribution[n,p]]

Hustota:

?PDF

PDF[BinomialDistribution[n,p],x]

DiscretePlot[PDF[BinomialDistribution[30,1/2],x],{x,0,30}]

PDF[NormalDistribution[μ,σ],x]

Plot[PDF[NormalDistribution[2,3],x],{x,-5,10}]

Distribuční funkce, kvantily, inverzní distribuční funkce:

?CDF

Plot[CDF[NormalDistribution[0,1],x],{x,-3,3}]

Quantile[NormalDistribution[0,1],.95]

Quantile[rozdělení,q]je totéž jako InverseCDF[rozdělení,q].

Plot[InverseCDF[NormalDistribution[0,1],x],{x,0,1}]

Výpočet pravděpodobnosti:

?Probability

Symbol \[Distributed] se vkládá jako EscdistEsc.

Jaká je pravděpodobnost, že při 100 hodech mincí bude počet líců mezi 60 a 80?

Probability[60≤x≤80,x\[Distributed]BinomialDistribution[100,1/2]]

N[%]

Jaká je pravděpodobnost, že při pěti hodech kostkou dostaneme součet 20?

pocetKostek=5;
Probability[Sum[x[i],{i,1,pocetKostek}]==20,Table[x[i]\[Distributed]DiscreteUniformDistribution[{1,6}],{i,1,pocetKostek}]]

Pro větší počty kostek (a obecněji větší počty náhodných proměnných) trvá výpočet dlouho, případně skončí vyčerpáním paměti. Vysvětlení:

For a discrete distribution dist, the probability of pred is given by ∑Boole[pred]f[x] where f[x] is the probability density function of dist and the summation is taken over the domain of dist.

For a continuous distribution dist, the probability of pred is given by ∫Boole[pred]f[x]dx where f[x] is the probability density function of dist and the integral is taken over the domain of dist.

Jaká je pravděpodobnost, že kvadratický polynom bude mít reálné kořeny, jestliže koeficienty vybereme náhodně z intervalu [0,1]?

Probability[Discriminant[a x^2+b x+c,x]≥0,{a,b,c}\[Distributed]UniformDistribution[{{0,1},{0,1},{0,1}}]]

N[%]

Podmíněná pravděpodobnost (symbol \[Conditioned] se zapisuje pomocí EsccondEsc):

Probability[x==2\[Conditioned]x+y==5,{x\[Distributed]DiscreteUniformDistribution[{1,6}],y\[Distributed]DiscreteUniformDistribution[{1,6}]}]
(* Pravděpodobnost, že při hodu dvěma kostkami padne na první hodnota 2, a to za předpokladu, že součet je 5. *)

Generování náhodných čísel ze zadaného rozdělení:

data=RandomVariate[NormalDistribution[2,1],10000];

Mean[data]

Variance[data]

hist=Histogram[data,Automatic,"ProbabilityDensity"]

Show[hist,Plot[PDF[NormalDistribution[2,1],x],{x,-10,10},PlotRange->All]]

Zpětné určení parametrů rozdělení metodou maximální věrohodnosti:

FindDistributionParameters[data,NormalDistribution[μ,σ]]

EstimatedDistribution[data,NormalDistribution[μ,σ]]

Vizualizace dat pomocí krabicového diagramu:

data1=RandomInteger[{80,120},10]

data2=RandomInteger[{80,120},10]

data3=RandomInteger[{80,120},10]

BoxWhiskerChart[{data1,data2,data3}]

BoxWhiskerChart[{data1,data2,data3},ChartStyle->10,BarOrigin->Left,BaseStyle->12]

Benfordův zákon

Citace z Wikipedie:

Benfordův zákon je matematický zákon, který říká, že v mnoha souborech přirozených dat (ale ne ve všech) čísla mnohem častěji začínají cifrou 1 než jinými ciframi. Zhruba 30 % čísel začíná jedničkou. Čím vyšší je počáteční číslice, tím méně pravděpodobněji se na začátku čísel objevuje.

Benfordův zákon platí pro data z přírodního světa nebo i pro sociálně významné údaje. ... Protože lidé mají tendenci při vymýšlení falešných výsledků používat na začátku čísel všechny číslice stejně pravděpodobně, Benfordův zákon se může využívat při hledání možných zpronevěr nebo k jednoduchému testu, zda volby byly regulérní.

Pro dostatečnou platnost zákona stačí mít výsledky v rozsahu alespoň tří řádů.

Poprvé o tomto zákonu publikoval v roce 1881 americký astronom Simon Newcomb, který si prý všiml, že logaritmické tabulky jsou mnohem ohmatanější na stránkách, kde se vyskytují čísla začínající jedničkou. Zákon byl znovuobjeven roku 1938 fyzikem Frankem Benfordem, podle kterého se dnes nazývá.

BenfordDistribution[b] je Benfordovo rozdělení pro soustavu o základu b.

Pravděpodobnost počáteční číslice n∈{1,...,b-1} je (Subscript[log, b])(n+1)-(Subscript[log, b])n=((log(1+1/n))/(log b)).

Table[PDF[BenfordDistribution[10],x],{x,1,9}]

N[%]

benford=DiscretePlot[PDF[BenfordDistribution[10],x],{x,1,9},PlotStyle->PointSize[Medium]]

FirstDigit[x_]:=First[First[RealDigits[QuantityMagnitude[x],10,1]]];

sample=Table[FirstDigit[CityData[city,"Population"]],{city,CityData[{All,"UnitedStates"}]}];

Show[Histogram[sample,{0.5,9.5,1},"PDF"],benford]

sample2=Table[FirstDigit[CityData[city,"Population"]],{city,CityData[{All,"CzechRepublic"}]}];

Show[Histogram[sample2,{0.5,9.5,1},"PDF"],benford]

sample3=Table[FirstDigit[CountryData[country,"Area"]],{country,CountryData[All]}];

Show[Histogram[sample3,{0.5,9.5,1},"PDF"],benford]

sample4=DeleteCases[Table[FirstDigit[CountryData[country,"GDP"]],{country,CountryData[All]}],"NotAvailable"];

Show[Histogram[sample4,{0.5,9.5,1},"PDF"],benford]

Benfordův zákon se nevztahuje na seznamy čísel, která jsou zhruba stejného řádu:

sample5=Table[CityData[city,"Population"],{city,Take[CityData[{All,"UnitedStates"}],100]}];

Min[sample5]

Max[sample5]

Show[Histogram[Map[FirstDigit,sample5],{0.5,9.5,1},"PDF"],benford]

Mapy a geografické výpočty

Mapa světa:

GeoGraphics[GeoRange->"World",ImageSize->Large]

Nastavení pozadí pomocí GeoBackground (“VectorClassic” je vektorový obrázek místo bitmapového):

Table[GeoGraphics[GeoRange->"World",GeoBackground->background, ImageSize->Large,PlotLabel->background],{background,{"VectorClassic","ContourMap","ReliefMap","Satellite","SatelliteWithLabels","CountryBorders","StreetMap"}}]

Výběr kartografické projekce pomocí GeoProjection:

Table[GeoGraphics[GeoRange->"World",GeoProjection->projection,GeoGridLines->Automatic,ImageSize->Large,PlotLabel->projection,GeoBackground->"StreetMapNoLabels"],{projection,{"Mercator","LambertCylindrical","Orthographic","Albers","LambertAzimuthal","Stereographic"}}]

Zobrazení mapy vybrané oblasti:

GeoGraphics[GeoPosition[{50.08,14.43}],ImageSize->Large]

Table[GeoGraphics[GeoPosition[{50.08,14.43}],GeoZoomLevel->zoom,ImageSize->Large],{zoom,{3,5,8,11,15,18}}]

Zjištění zeměpisných souřadnic z názvu města (vstup v přirozeném jazyce pomocí Ctrl + =):

GeoPosition[LinguisticAssistant]

Entity zadané v přirozeném jazyce mohou být součástí GeoGraphics:

GeoGraphics[LinguisticAssistant]

Do mapy lze doplňovat další grafické objekty:

GeoGraphics[{EdgeForm[{Blue,Thick}],Polygon[LinguisticAssistant],White,PointSize[Large],Point[LinguisticAssistant]},GeoBackground->"Satellite"]

Velká německá města:

cities=CityData[{Large,"Germany"}];
populations=QuantityMagnitude[Map[CityData[#,"Population"]&,cities]];
coordinates=Map[CityData[#,"Coordinates"]&,cities];
large=Cases[Transpose[{cities,populations,coordinates}],{_,u_,_}/;u≥500000]

largeCoordinates=Map[Last,large]

GeoGraphics[{Polygon[LinguisticAssistant],PointSize[Large],Red,Point[Map[GeoPosition,largeCoordinates]]}]

Místo bodů lze použít GeoMarker:

GeoGraphics[{GeoStyling["StreetMapNoLabels",EdgeForm[Black]],Polygon[LinguisticAssistant],GeoMarker[Map[GeoPosition,largeCoordinates],"Alignment"->Bottom]},GeoBackground->None]

Uživatelem definovaný vzhled značky:

marker[color_]:=Graphics[GraphicsGroup[{FaceForm[color],EdgeForm[Black],FilledCurve[{{Line[Join[{{0,0}},({Cos[#1],3+Sin[#1]}&)/@Range[-((2 π)/20),π+((2 π)/20),(π/20)],{{0,0}}]]},{Line[(0.5 {Cos[#1],6+Sin[#1]}&)/@Range[0,2 π,(π/20)]]}}]}]]

marker[Yellow]

GeoGraphics[{GeoStyling["StreetMapNoLabels",EdgeForm[Black]],Polygon[LinguisticAssistant],GeoMarker[Map[GeoPosition,largeCoordinates],marker[Red],"Alignment"->Bottom]},GeoBackground->None]

Geodetika (nejkratší spojnice) a loxodroma mezi zadanými dvěma místy:

stockholm=GeoPosition[LinguisticAssistant]

ottawa=GeoPosition[LinguisticAssistant]

GeoGraphics[{GeoMarker[{stockholm,ottawa},marker[Red],"Alignment"->Bottom],Thick,Red,GeoPath[{stockholm,ottawa}],Blue,GeoPath[{stockholm,ottawa},"Loxodrome"]},GeoRange->{{-60,80},{-180,180}},ImageSize->Large,GeoProjection->"Mercator"]

GeoDistance[{stockholm,ottawa}]

Toto je vzdálenost mezi hranicemi měst:

GeoDistance[{LinguisticAssistant,LinguisticAssistant}]

Toto je vzdálenost středů měst:

GeoDistance[{LinguisticAssistant,LinguisticAssistant},DistanceFunction->"Center"]

GeoDistance[{GeoPosition[LinguisticAssistant],GeoPosition[LinguisticAssistant]}]

Geodetický kruh se zadaným poloměrem:

GeoGraphics[{EdgeForm[{Black,Dashed}],GeoDisk[LinguisticAssistant,Quantity[20,"km"]]}]

GeoNearest["City",LinguisticAssistant,{All,Quantity[20,"km"]}]

Mercatorova projekce nezachovává obsahy ploch:

GeoGraphics[{Table[GeoDisk[{lat,lon},(Quantity[1000, "km", kilometers, "Kilometers"])],{lat,-60,60,30},{lon,-160,160,40}]},GeoProjection->"Mercator"]

Lambertova válcová projekce zachovává obsahy ploch:

GeoGraphics[{Table[GeoDisk[{lat,lon},(Quantity[1000, "km", kilometers, "Kilometers"])],{lat,-60,60,30},{lon,-160,160,40}]},GeoProjection->"LambertCylindrical"]

Osvětlená a neosvětlená část Země:

GeoGraphics[NightHemisphere[Now],GeoRange->"World",ImageSize->Large]

Buněčné automaty (CellularAutomaton)

Podrobnější informace: Stephen Wolfram, A New Kind of Science. Wolfram Media, Inc., 2002. Také online na http://www.wolframscience.com/nksonline/.

Automat = množina buněk

Každá buňka se nachází v jednom z konečně mnoha stavů

Výpočet automatu probíhá v krocích, stav buňky v dalším kroku je určen jejím aktuálním stavem a stavem jejích sousedů (přechodová funkce)

Nejjednodušší typ buněčného automatu

Buňky se dvěma stavy 0 a 1, tj. stav automatu = vektor obsahující nuly a jedničky (bílá a černá barva)

Přechodová funkce bere v úvahu pouze nejbližší dvě sousední buňky

Příklad 1:

RulePlot[CellularAutomaton[254]]

Buňka bude v dalším kroku černá, pokud již je černá nebo má aspoň jednoho černého souseda.

Každé pravidlo je jednoznačně určeno číslem 0 až 255 (číslo dostaneme tak, že spodní řádek předchozího obrázku interpretujeme jako dvojkový zápis tohoto čísla).

?CellularAutomaton

(c254=CellularAutomaton[254,{{1},0},6])//TableForm

ArrayPlot[c254,Mesh->True]

Příklad 2:

RulePlot[CellularAutomaton[250]]

Buňka bude v dalším kroku bílá, právě když oba její sousedé jsou bílí.

FromDigits[{1,1,1,1,1,0,1,0},2]

ArrayPlot[CellularAutomaton[250,{{1},0},6],Mesh->True]

Příklad 3:

RulePlot[CellularAutomaton[90]]

Buňka bude v dalším kroku černá, právě když má přesně jednoho černého souseda.

FromDigits[{0,1,0,1,1,0,1,0},2]

ArrayPlot[CellularAutomaton[90,{{1},0},6],Mesh->True]

Manipulate[ArrayPlot[CellularAutomaton[90,{{1},0},n],ImageSize->Large],{n,10,500,1,Appearance->"Labeled"}]

Příklad 4:

RulePlot[CellularAutomaton[30]]

Pokud jsou buňka a její pravý sousedí bílí, bude barva změněna na barvu levého souseda, jinak na barvu opačnou.

FromDigits[{0,0,0,1,1,1,1,0},2]

Manipulate[ArrayPlot[CellularAutomaton[30,{{1},0},n],ImageSize->Large],{n,10,500,1,Appearance->"Labeled"}]

What you find is there is a certain amount of regularity you can see over on the left, for example. But in many respects this picture looks extremely complicated and in a sense seemingly random. In fact, for example as a practical matter, the randomness of this is sufficiently good that if you take the center column of this thing and you wrap it around in a finite-size register and all that kind of thing, you can use that center column as a way of generating randomness.
And in fact, the Random function in Mathematica, Random[Integer], has used this method for generating randomness ever since Mathematica Version 1 was released. And it has been a really good method of generating randomness. In fact it has been an embarrassment to us that for some real number random generation methods we used, against my better judgment I was convinced that we should use more traditional random generators, which were slightly faster at the time when these things were first implemented but which have turned out to have all kinds of horrible bugs. So, this particular way of generating randomness, this little rule 30 thing, which is by far the simplest in terms of its rule, has withstood all of these attacks.

(Stephen Wolfram, The Future of Computation. The Mathematica Journal, vol. 10, issue 2)

Příklad 5:

RulePlot[CellularAutomaton[110]]

FromDigits[{0,1,1,0,1,1,1,0},2]

ArrayPlot[CellularAutomaton[110,{{1},0},300],ImageSize->Large]

Katalog všech automatů (každý začíná ve stavu s jednou černou buňkou):

GraphicsGrid[Partition[Map[ArrayPlot[CellularAutomaton[#,{{1},0},{40,All}],PlotLabel->#]&,Range[0,255]],8],ImageSize->Full]

Zadání automatu 90 pomocí přepisovacích pravidel:

ArrayPlot[CellularAutomaton[{{1,_,1}->0,{1,_,0}->1,{0,_,1}->1,{0,_,0}->0},{{1},0},50]]

Zadání automatu pomocí funkce, která se aplikuje na seznam sousedů:

ArrayPlot[CellularAutomaton[{Mod[#[[1]]+#[[3]],2]&,{},1},{{1},0},50]]

Obecnější typy automatů

Automaty, jejichž přechodová funkce závisí na širším okolí (tj. na větším počtu sousedů)

"Vícebarevné automaty" (buňka má více než 2 přípustné stavy)

Dvou- a vícerozměrné automaty

Příklad: Trojbarevný automat s číslem 679458:

RulePlot[CellularAutomaton[{679458, 3}]]

FromDigits[{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,2,1,1,1,2,0,0,1,0,1,0},3]

ArrayPlot[CellularAutomaton[{679458, 3}, {{1}, 0}, 10],Mesh->True]

Příklad: Dvourozměrný dvoubarevný automat simulující Conwayovu hru života (Game of Life)

LifeConfigurations={{{0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0,0},{0,0,0,1,0,1,0,0,0,0,0,0,1,0,1,0,0,0},{0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0},{1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,1,1},{1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,1},{0,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0},{0,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0},{1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,1},{1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,1,1},{0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0},{0,0,0,1,0,1,0,0,0,0,0,0,1,0,1,0,0,0},{0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0,0}}->"101",
{{0,0,0,1,0,0,0,0},{0,0,1,0,1,0,0,0},{0,1,0,1,1,0,0,0},{1,0,1,0,0,1,1,0},{0,1,1,0,0,1,0,1},{0,0,0,1,1,0,1,0},{0,0,0,1,0,1,0,0},{0,0,0,0,1,0,0,0}}->"4 boats",
{{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1},{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1},{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1}}->"Achim's p144",{{0,0,1,1,0,0,0,1,1,0,0},{0,1,0,0,1,0,1,0,0,1,0},{0,1,0,1,1,0,1,1,0,1,0},{1,1,0,0,0,0,0,0,0,1,1},{0,0,1,0,1,0,1,0,1,0,0},{1,1,0,0,0,0,0,0,0,1,1},{0,1,0,1,1,0,1,1,0,1,0},{0,1,0,0,1,0,1,0,0,1,0},{0,0,1,1,0,0,0,1,1,0,0}}->"Achim's p4",
{{0,1,0,0,0,0,0},{0,0,0,1,0,0,0},{1,1,0,0,1,1,1}}->"acorn",{{0,0,0,0,1,1,0,0,0,0},{0,0,0,1,0,0,1,0,0,0},{0,0,0,1,1,1,1,0,0,0},{0,1,0,1,0,0,1,0,1,0},{1,0,0,0,0,0,0,0,0,1},{1,0,0,0,0,0,0,0,0,1},{0,1,0,1,0,0,1,0,1,0},{0,0,0,1,1,1,1,0,0,0},{0,0,0,1,0,0,1,0,0,0},{0,0,0,0,1,1,0,0,0,0}}->"A for All",{{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1}}->"agar",{{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1}}->"agar virus eliminated",{{1,1,0,0},{1,0,0,1},{0,0,1,1}}->"aircraft carrier",{{0,0,0,0,0,0,0,1,0,0,0,0,0,0},{0,0,0,0,0,0,1,0,1,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,1,1,1,1,1,0,0,0,0},{0,0,0,0,1,0,0,0,0,0,1,0,1,1},{0,0,0,1,0,1,1,0,0,0,1,0,1,1},{0,0,0,1,0,1,0,0,1,0,1,0,0,0},{1,1,0,1,0,0,0,1,1,0,1,0,0,0},{1,1,0,1,0,0,0,0,0,1,0,0,0,0},{0,0,0,0,1,1,1,1,1,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,1,0,0,0,0,0,0,0},{0,0,0,0,0,1,0,1,0,0,0,0,0,0},{0,0,0,0,0,0,1,0,0,0,0,0,0,0}}->"airforce",{{0,0,0,0,0,1,0,0,0,0},{0,0,0,0,1,0,1,0,0,0},{0,0,0,1,0,0,0,1,0,0},{0,0,0,1,0,0,0,1,0,0},{0,0,0,1,0,0,0,1,0,0},{0,0,0,0,1,0,1,0,0,0},{0,0,0,0,0,1,0,0,0,0},{0,0,0,0,0,0,0,0,0,0},{0,0,1,1,0,0,0,0,0,0},{0,0,0,1,0,0,0,0,0,0},{1,1,1,0,0,0,0,0,1,1},{1,0,0,0,0,0,0,0,1,1}}->"AK47 reaction",{{1,1,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0},{0,0,1,1,0,1,1,0,0,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1},{0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1},{1,1,0,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0,0,1,1,0,0},{0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}->"ants",{{0,0,0,0,0,1,0,0,0,0,0},{0,0,0,0,1,0,1,0,0,0,0},{0,0,0,0,0,1,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,1,1,1,1,0,0,0},{0,0,1,0,0,1,0,0,1,0,0},{0,1,0,1,1,0,1,1,0,1,0},{0,1,0,1,0,0,0,1,0,1,0},{1,1,0,1,0,0,0,1,0,1,1},{1,0,0,1,0,1,0,1,0,0,1},{0,0,1,0,0,0,0,0,1,0,0},{0,0,0,1,1,1,1,1,0,0,0},{0,0,0,0,0,1,0,0,0,0,0}}->"aVerage",{{0,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0},{1,0,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}->"B",{{1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0},{1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0},{1,0,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,1},{0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,0,1,1,1,1},{0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,1}}->"baker's dozen",{{0,0,0,0,1,1,0,0,0,0},{0,0,0,1,0,0,1,0,0,0},{0,0,0,1,0,1,0,0,0,0},{0,1,1,0,1,0,0,0,1,0},{1,0,0,1,0,0,0,1,0,1},{1,0,1,0,0,0,1,0,0,1},{0,1,0,0,0,1,0,1,1,0},{0,0,0,0,1,0,1,0,0,0},{0,0,0,1,0,0,1,0,0,0},{0,0,0,0,1,1,0,0,0,0}}->"bakery",{{0,0,0,0,0,1,1},{0,0,0,0,0,0,1},{0,0,0,1,0,1,0},{0,0,0,0,0,0,0},{0,1,0,1,0,0,0},{1,0,0,0,0,0,0},{1,1,0,0,0,0,0}}->"barberpole",{{0,1,0,0},{1,0,1,0},{0,1,0,1},{0,0,1,0}}->"barge",{{1,1,0,0},{1,0,0,0},{0,0,0,1},{0,0,1,1}}->"beacon",{{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0}}->"beacon maker",{{0,1,1,0},{1,0,0,1},{0,1,1,0}}->"beehive",{{1,1,0,0,1,1},{1,0,0,0,0,1},{0,1,1,1,1,0},{0,0,0,0,0,0},{0,0,0,1,1,0},{0,0,1,0,0,1},{0,0,0,1,1,0}}->"beehive and dock",{{0,1,0,0,0},{1,0,1,0,0},{1,0,1,0,0},{0,1,0,0,0},{0,0,1,1,1},{0,0,0,0,1}}->"beehive with tail",
{{1,0,1,1},{1,1,1,0},{0,1,0,0}}->"B-heptomino",{{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1},{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,0,0,1,0,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0},{0,1,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0},{0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}->"B-heptomino shuttle",{{1,1,0,1,1},{1,1,0,1,1}}->"biblock",{{0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0},{1,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0},{0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,0,0,1,0,0,0,0,0,1,0,1,1,0,0,0,0},{0,1,0,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0},{0,0,0,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0},{0,0,0,0,1,1,0,1,0,0,0,0,1,1,0,0,0,1},{0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0},{0,0,0,0,0,0,0,1,1,1,1,0,0,0,1,0,1,0},{0,0,0,0,0,0,0,1,0,1,1,0,0,0,1,1,1,1},{0,0,0,0,0,0,0,0,1,0,0,0,1,1,0,1,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0},{0,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0}}->"big glider",{{0,0,0,0,1,1,0},{0,0,0,1,0,0,1},{0,0,0,1,0,1,1},{1,1,0,1,0,0,0},{1,0,0,1,0,0,0},{0,1,1,0,0,0,0}}->"big S",{{0,1,0,0,0,0,0},{1,0,1,0,0,0,0},{1,0,0,1,0,0,0},{0,1,1,0,1,0,0},{0,0,0,1,0,1,0},{0,0,0,1,0,0,1},{0,0,0,0,1,1,0}}->"biloaf",{{1,1,0,0,0},{1,0,1,0,0},{0,0,0,0,0},{0,0,1,0,1},{0,0,0,1,1}}->"bipole",{{0,1,1,0,0,0,0},{1,0,0,1,0,0,0},{1,0,0,1,0,0,0},{0,1,1,0,1,1,0},{0,0,0,1,0,0,1},{0,0,0,1,0,0,1},{0,0,0,0,1,1,0}}->"bipond",{{0,0,0},{1,1,1},{0,0,0}}->"blinker",{{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,1,0,0,0,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,1,1,1},{0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,1},{0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,1,1,1},{0,1,1,0,0,0,0,0,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}->"blinker ship",{{1,1},{1,1}}->"block",{{1,1,0,0,1,1},{1,0,0,0,0,1},{0,1,1,1,1,0},{0,0,0,0,0,0},{0,0,0,1,1,0},{0,0,0,1,1,0}}->"block and dock",{{1,1,0,0},{1,0,1,0},{0,0,1,1}}->"block and glider",{{0,0,0,0,0,0,1,0,1,0},{0,0,0,0,0,1,0,0,0,0},{1,1,0,0,1,0,0,0,0,1},{1,1,0,1,0,0,1,0,1,1},{0,0,0,0,1,1,0,0,0,0}}->"blocker",{{1,1,0,0,0},{0,1,0,0,0},{0,1,0,1,1},{1,1,0,1,1}}->"block on table",{{0,1,0},{1,0,1},{0,1,1}}->"boat",{{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0}}->"boat maker",{{0,1,0,0,0,0},{1,0,1,0,0,0},{0,1,1,0,0,0},{0,0,0,1,1,0},{0,0,0,1,0,1},{0,0,0,0,1,0}}->"boat on boat",{{1,1,0,0,0,0},{1,0,1,0,0,0},{0,1,1,0,0,0},{0,0,0,1,1,0},{0,0,0,1,0,1},{0,0,0,0,1,0}}->"boat-ship-tie",{{1,1,0,0,0,1,1},{1,0,1,0,1,0,1},{0,0,1,0,1,0,0},{0,1,1,0,1,1,0}}->"bookends",{{0,0,0,0,0,1,0,0,0,0,0},{0,0,0,0,1,0,1,0,0,0,0},{0,0,0,0,1,0,1,0,0,0,0},{0,0,0,1,1,0,1,1,0,0,0},{0,0,1,0,0,0,0,0,1,0,0},{0,1,0,1,0,1,0,1,0,1,0},{0,1,0,1,0,0,0,1,0,1,0},{1,1,0,1,0,0,0,1,0,1,1},{1,0,0,1,0,1,0,1,0,0,1},{0,0,1,0,0,0,0,0,1,0,0},{0,0,0,1,1,0,1,1,0,0,0},{0,0,0,0,1,0,1,0,0,0,0},{0,0,0,0,1,0,1,0,0,0,0},{0,0,0,0,0,1,0,0,0,0,0}}->"boss",{{0,1,1,0,0,0,0,0,0,0,0},{1,0,0,1,0,0,0,0,0,1,1},{1,1,1,0,0,0,1,1,1,0,0},{1,0,0,1,0,1,1,1,1,0,0},{0,1,1,1,0,0,0,1,0,0,0},{0,1,0,0,1,1,1,0,0,0,0},{0,0,0,1,0,0,0,0,1,1,0},{0,0,0,1,1,1,1,1,0,1,0},{0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,1,1,1,1,0,1,0},{0,0,0,1,0,0,0,0,1,1,0},{0,1,0,0,1,1,1,0,0,0,0},{0,1,1,1,0,0,0,1,0,0,0},{1,0,0,1,0,1,1,1,1,0,0},{1,1,1,0,0,0,1,1,1,0,0},{1,0,0,1,0,0,0,0,0,1,1},{0,1,1,0,0,0,0,0,0,0,0}}->"brain",{{0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1},{0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1},{0,0,0,1,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,1,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}->"buckaroo",{{1,0,0,0,0,0,1,0},{0,0,1,0,0,0,1,0},{0,0,1,0,0,1,0,1},{0,1,0,1,0,0,0,0}}->"bunnies",{{0,0,0,0,0,1,0,0,0,0,0},{0,0,0,0,1,0,1,0,0,0,0},{0,0,0,1,0,1,0,1,0,0,0},{0,0,0,1,0,1,0,1,0,0,0},{1,1,0,1,0,1,0,1,0,1,1},{1,1,0,1,0,0,0,0,1,0,1},{0,0,0,0,1,1,1,1,0,0,0},{0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,1,0,0,0,0,0},{0,0,0,0,1,1,0,0,0,0,0}}->"burloaf",{{1,1,1,0,0,0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0,0,0,1,1,0},{0,1,0,0,0,0,0,0,1,1,1,0,1},{0,0,0,1,1,0,0,1,1,0,0,0,0},{0,0,0,0,1,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,1,0,0,0,0},{0,0,0,0,1,1,0,0,0,1,0,0,0},{0,0,0,1,0,1,0,1,1,0,0,0,0},{0,0,0,1,0,1,0,0,1,0,1,1,0},{0,0,1,0,0,0,0,1,1,0,0,0,0},{0,0,1,1,0,0,0,0,0,0,0,0,0},{0,0,1,1,0,0,0,0,0,0,0,0,0}}->"Canada goose",{{0,0,0,1,1},{0,0,0,0,1},{0,0,0,1,0},{1,0,1,0,0},{1,1,0,0,0}}->"canoe",{{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1},{1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1},{0,1,0,1,0,1,0,0,0,1,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,0},{0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0,1,0,1,0},{0,1,0,1,0,1,0,0,0,1,0,0,1,0,0,0,0,0,0,1,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,0},{1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1}}->"carnival shuttle",{{0,0,0,0,0,1,0,0},{1,1,1,1,0,0,0,1},{0,0,0,1,0,0,0,1},{0,0,0,0,0,0,0,1},{0,0,0,0,1,0,0,0},{0,0,0,0,0,1,1,0}}->"caterer",{{0,0,0,0,0,1,0,0,0,0,0},{0,0,0,0,1,0,1,0,0,0,0},{0,0,0,0,0,1,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,1,1,1,1,0,0,0},{1,0,1,0,0,0,0,0,1,0,1},{1,1,0,1,0,0,0,1,0,1,1},{0,0,0,1,0,0,0,1,0,0,0},{0,0,0,1,0,0,0,1,0,0,0},{0,0,0,0,1,1,1,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,1,0,1,0,0,0},{0,0,0,0,1,0,1,1,0,0,0}}->"cauldron",{{1,1,0,0,0,0,0,0},{0,1,0,0,0,0,0,0},{0,1,0,1,1,0,0,0},{0,0,1,0,0,1,0,0},{0,0,0,0,0,1,0,0},{0,0,0,0,1,0,0,0},{0,0,0,0,0,1,1,1},{0,0,0,0,0,0,0,1}}->"cavity",{{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0},{0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0},{0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0},{0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0},{0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0},{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1}}->"centinal",{{0,0,1,1},{1,1,1,0},{0,1,0,0}}->"century",{{0,0,0,1,1,0,0,0,0,0,1,1,0,0,0},{0,0,0,1,0,0,0,0,0,0,0,1,0,0,0},{1,1,0,1,0,0,0,0,0,0,0,1,0,1,1},{1,0,0,1,1,0,0,0,0,0,1,1,0,0,1},{0,1,1,0,0,0,1,0,0,0,0,0,1,1,0},{0,0,0,1,1,0,0,0,1,1,1,1,0,0,0},{0,0,0,1,0,0,0,0,0,0,0,1,0,0,0},{0,0,0,0,1,1,1,1,1,1,1,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,1,1,1,0,0,0,0,0,0},{0,0,0,0,0,0,1,0,0,1,0,0,0,0,0},{0,0,0,0,0,0,0,0,1,1,0,0,0,0,0}}->"champagne Glass",{{0,0,0,0,0,0,0,1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,1,1,1,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0},{0,0,0,0,0,1,1,1,0,0,1,0,0,1,1},{0,0,0,0,1,0,1,0,1,0,1,0,1,0,1},{0,0,0,0,1,0,0,0,1,0,1,0,1,0,0},{0,1,1,0,1,0,1,0,1,0,1,0,1,1,0},{0,0,1,0,1,0,1,0,0,0,1,0,0,0,0},{1,0,1,0,1,0,1,0,1,0,1,0,0,0,0},{1,1,0,0,1,0,0,1,1,1,0,0,0,0,0},{0,0,0,0,1,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,1,1,1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,0,0,0,0,0,0}}->"chemist",{{0,1,1,1},{1,1,1,0},{0,1,0,0}}->"C-heptomino",{{0,1,0,0,1,0},{0,1,1,1,1,0},{1,0,0,0,0,1},{1,0,1,1,0,1},{1,0,0,0,0,1},{0,1,1,1,1,0}}->"Cheshire cat",{{0,0,0,1,1,0,0},{0,0,0,0,1,0,0},{0,1,0,0,0,0,0},{0,1,1,0,0,0,0},{0,0,0,0,0,0,0},{0,1,1,1,1,0,0},{1,0,0,0,0,1,0},{0,1,1,1,0,1,0},{0,0,0,1,0,1,1}}->"cis-beacon on anvil",{{0,0,1,1},{0,0,0,1},{1,0,0,0},{1,1,0,0},{0,0,0,0},{1,1,1,1},{1,0,0,1}}->"cis-beacon on table",{{0,0,0,0,1},{0,0,1,1,1},{0,1,0,0,0},{1,0,1,0,0},{0,1,1,0,0}}->"cis-boat with 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ship",{{0,0,0,0,0,0,0,0,0,1,1,0,1},{1,0,1,1,0,0,0,0,0,0,1,1,1},{1,1,0,1,0,0,0,0,0,0,0,1,0},{0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,1,1,0,0},{0,0,0,0,0,0,0,0,0,1,1,0,0}}->"conduit",{{1,0,0,0,0,0,0,0,0,0,0},{1,1,1,0,0,0,0,0,0,0,0},{0,0,0,1,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0,0,0},{0,0,1,0,0,1,0,0,0,0,0},{0,0,0,0,0,1,0,0,0,0,0},{0,0,0,1,0,1,0,0,0,0,0},{0,0,0,1,1,0,0,1,1,0,0},{0,0,0,0,0,0,0,1,0,1,0},{0,0,0,0,0,0,0,0,0,1,0},{0,0,0,0,0,0,0,0,0,1,1}}->"confused 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{{0,0,1,0,0},{0,1,0,1,0},{0,1,0,1,0},{1,1,0,1,1}}->"hat",{{0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0},{0,0,1,1,0,1,0,0,0,0,1,0,1,1,0,0},{0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0},{0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0},{1,1,1,0,0,1,1,1,1,1,1,0,0,1,1,1},{1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1},{0,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0}}->"heavyweight emulator",{{0,1,1,1,1,1,1},{1,0,0,0,0,0,1},{0,0,0,0,0,0,1},{1,0,0,0,0,1,0},{0,0,1,1,0,0,0}}->"heavyweight 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volcano",{{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0},{1,0,1,1,0,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0},{1,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,1,0,1,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,1,1,0,0,0,0,1,1,0},{0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,1,1,1,0,0,0,0,0,1,0,0,0,0,0,0,1,1}}->"Heptominoes",{{1,0,0},{1,1,1},{1,0,1},{0,0,1}}->"Herschel",{{0,0,0,1,1,0,1,0,0,0,0},{0,0,0,1,0,1,1,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,1,1,0,0,0,0},{0,0,0,1,0,1,0,1,0,1,1},{0,0,0,1,0,0,0,1,0,1,1},{1,1,0,1,0,0,0,1,0,0,0},{1,1,0,1,0,0,0,1,0,0,0},{0,0,0,0,1,1,1,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,1,0,1,0,0,0},{0,0,0,0,1,0,1,1,0,0,0}}->"Hertz oscillator",{{0,0,0,0},{0,0,0,0},{0,0,0,0},{1,1,1,0},{0,0,0,1},{0,0,0,1},{0,0,0,1}}->"HighLife",{{1,1,1,1,0,0,0,0,0,1,0,0,1},{1,0,0,0,1,0,0,0,1,0,0,0,0},{1,0,0,0,0,0,0,0,1,0,0,0,1},{0,1,0,0,1,0,0,0,1,1,1,1,0},{0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,1,1,0,0,0,0,0,0},{0,0,0,0,0,1,1,0,0,0,0,0,0},{0,0,0,0,0,1,1,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,0,0,1,0,0,0,1,1,1,1,0},{1,0,0,0,0,0,0,0,1,0,0,0,1},{1,0,0,0,1,0,0,0,1,0,0,0,0},{1,1,1,1,0,0,0,0,0,1,0,0,1}}->"hivenudger",{{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1},{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1},{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1}}->"Hockey 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reaction",{{0,0,1,1,0,0,0,0,0,0,0,1,1,1},{1,0,0,0,0,1,0,0,0,0,1,1,1,0},{0,0,0,0,0,0,1,0,0,0,0,0,0,0},{1,0,0,0,0,0,1,0,0,0,0,0,0,0},{0,1,1,1,1,1,1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,1,1,0},{0,0,0,0,0,0,0,0,0,0,0,1,1,1}}->"killer toads",{{1,1,1,1,1,1,0,1,1},{1,1,1,1,1,1,0,1,1},{0,0,0,0,0,0,0,1,1},{1,1,0,0,0,0,0,1,1},{1,1,0,0,0,0,0,1,1},{1,1,0,0,0,0,0,1,1},{1,1,0,0,0,0,0,0,0},{1,1,0,1,1,1,1,1,1},{1,1,0,1,1,1,1,1,1}}->"Kok's galaxy",{{0,0,0,0,1,1,0,0,0,0},{0,0,0,1,0,0,1,0,0,0},{0,0,0,1,0,0,1,0,0,0},{0,1,1,0,0,0,0,1,1,0},{1,0,0,0,0,0,0,0,0,1},{1,0,0,0,0,0,0,0,0,1},{0,1,1,0,0,0,0,1,1,0},{0,0,0,1,0,0,1,0,0,0},{0,0,0,1,0,0,1,0,0,0},{0,0,0,0,1,1,0,0,0,0}}->"lake",{{0,1,1,0,1,0,0},{0,1,0,1,1,0,0},{0,0,0,0,0,0,0},{0,0,1,1,1,0,0},{0,1,0,0,0,1,0},{0,1,0,0,0,1,0},{0,0,1,0,1,0,0},{1,0,1,0,1,0,1},{1,1,0,0,0,1,1}}->"light 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of 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river",{{0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0},{0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0},{0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0},{0,1,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,0,0,1,0},{1,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,1},{0,1,0,0,1,0,0,0,0,1,0,1,0,0,0,0,0,1,0,1,0,0,0,0,1,0,0,1,0},{0,0,0,0,1,1,0,0,1,0,0,1,0,0,0,0,0,1,0,0,1,0,0,1,1,0,0,0,0},{0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0,1,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,1,0,0,0,1,0,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,1,1,0,0,0,0,0,0},{0,0,0,1,0,0,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0},{0,0,0,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}->"sailboat",{{0,0,0,0,0,1,1,1,1},{0,0,0,0,1,0,0,0,1},{0,0,0,0,0,0,0,0,1},{1,1,0,0,1,0,0,1,0},{1,1,1,0,0,0,0,0,0},{1,1,0,0,1,0,0,1,0},{0,0,0,0,0,0,0,0,1},{0,0,0,0,1,0,0,0,1},{0,0,0,0,0,1,1,1,1}}->"Schick engine",{{0,0,0,1,0,0,0},{0,1,1,1,0,0,0},{1,0,0,0,1,1,0},{1,0,1,0,1,0,1},{0,1,1,0,1,0,1},{0,0,0,0,0,1,0}}->"scorpion",{{0,0,0,0,1,0,0,0,0,0,0},{0,0,1,1,1,0,0,0,0,0,0},{0,1,0,0,0,0,0,0,0,0,0},{0,1,0,0,1,1,1,0,0,0,0},{1,1,0,1,0,0,0,1,0,0,0},{0,0,0,1,0,0,0,1,0,0,0},{0,0,0,1,0,0,0,1,0,1,1},{0,0,0,0,1,1,1,0,0,1,0},{0,0,0,0,0,0,0,0,0,1,0},{0,0,0,0,0,0,1,1,1,0,0},{0,0,0,0,0,0,1,0,0,0,0}}->"scrubber",{{1,1,0,0,0},{1,0,0,1,1},{0,1,1,0,1}}->"shillelagh",{{1,1,0},{1,0,1},{0,1,1}}->"ship",{{1,1,0,0,0,0},{1,0,1,0,0,0},{0,1,1,0,0,0},{0,0,0,1,1,0},{0,0,0,1,0,1},{0,0,0,0,1,1}}->"ship on ship",{{0,1,0,0,0,0,0,0},{1,0,0,0,0,0,1,0},{1,0,0,0,0,0,1,0},{1,1,1,1,1,0,1,0},{0,0,0,0,0,0,0,0},{0,0,0,0,1,1,0,0},{0,0,1,0,0,0,0,1},{0,1,0,0,0,0,0,0},{0,1,0,0,0,0,0,1},{0,1,1,1,1,1,1,0}}->"sidecar",{{0,1,1,0,1,1},{0,0,1,0,1,0},{0,1,0,0,1,0},{0,1,0,1,0,0},{1,1,0,1,1,0}}->"sidewalk",{{0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0},{0,0,0,1,1,0,0,0,0,0,1,0,1,0,0,0},{0,0,0,1,0,1,0,0,0,0,1,0,0,0,0,0},{0,0,0,0,0,1,0,0,0,1,1,0,1,0,0,0},{0,0,0,1,0,1,1,0,0,0,0,0,1,1,1,0},{0,1,1,1,0,0,0,0,0,1,0,1,0,0,0,1},{1,0,0,0,1,0,1,0,0,0,0,0,1,1,1,0},{0,1,1,1,0,0,0,0,0,1,1,0,1,0,0,0},{0,0,0,1,0,1,1,0,0,0,1,0,0,0,0,0},{0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,0},{0,0,0,1,0,1,0,0,0,0,0,1,1,0,0,0},{0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0}}->"siesta",{{0,1,1,0,0,0,0},{0,1,0,0,0,1,1},{0,0,1,0,1,0,1},{0,0,0,0,0,0,0},{1,0,1,0,1,0,0},{1,1,0,0,0,1,0},{0,0,0,0,1,1,0}}->"skewed quad",{{1,1,0,1,0,1,1},{0,0,0,1,0,0,0},{1,0,0,0,0,0,1},{0,1,1,1,1,1,0},{0,0,0,0,0,0,0},{0,0,0,0,0,0,0},{1,1,1,0,1,1,1}}->"smiley",{{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0},{0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0},{0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0},{0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0},{0,0,0,0,0,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0},{0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0},{0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0},{0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0},{1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1}}->"snacker",{{0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0},{0,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,1,1,1,0,0,0,0},{0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,1,0,1,0,0,0,0,0,1,1,0,0,0,0},{0,0,0,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,1},{0,0,0,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0},{0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0},{0,0,0,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,1},{0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,1,0,1,0,0,0,0,0,1,1,0,0,0,0},{0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,1,1,1,0,0,0,0},{0,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0},{0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,0},{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}->"snail",
{{1,0,1,1},{1,1,0,1}}->"snake",{{0,0,0,0,1,1},{0,0,0,0,1,0},{0,0,0,0,0,1},{0,0,0,0,1,1},{1,1,0,1,0,0},{1,0,1,1,0,0}}->"snake bridge snake",{{1,0,1,1,0,1,1},{1,1,0,1,0,1,0},{0,0,0,0,0,0,1},{1,1,1,0,1,1,1},{1,0,0,0,0,0,0},{0,1,0,1,0,1,1},{1,1,0,1,1,0,1}}->"snake pit",{{1,1,0,1,1,0,1},{1,0,1,1,0,1,1}}->"snake siamese snake",{{0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0},{0,0,0,1,0,1,0,0,0,0,0,0,1,0,1,0,0,0},{0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0},{0,0,0,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0},{0,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,1,0},{1,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,1},{0,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,1,0},{0,0,0,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0},{0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0},{0,0,0,1,0,1,0,0,0,0,0,0,1,0,1,0,0,0},{0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0}}->"sombreros",{{0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,1,1,1},{0,0,0,0,0,0,0,0,0,1,1,0,1,1,0,0,0,1,0,0,0,1},{0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,1},{0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,0,0,1,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,1,0,0,0},{0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0},{0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0},{0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,1,1,0,1,1,0,0},{0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1},{1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1},{0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1},{1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0},{0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}->"space rake",{{1,1,0,0,0,0,1,1},{1,0,1,0,0,1,0,1},{0,0,1,0,0,1,0,0},{1,0,1,0,0,1,0,1},{1,1,0,0,0,0,1,1}}->"spark coil",{{0,0,0,0,0,0,0,1,1},{0,0,0,0,0,0,1,0,1},{0,0,0,0,0,1,0,0,0},{0,0,0,0,1,0,0,0,0},{0,0,0,1,0,0,0,0,0},{0,1,1,1,0,0,0,0,0},{1,0,0,1,0,0,0,0,0},{0,1,1,0,0,0,0,0,0}}->"Spark Fuse",{{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0},{0,0,0,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0},{1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0},{1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,1},{1,0,1,1,0,0,0,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0,0,0},{0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1},{1,0,1,1,0,0,0,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0,0,0},{1,0,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0,1},{1,0,1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0,1,1,0,1,1,1,1,0,0,0,0,0,0},{0,0,0,0,0,0,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,0},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}->"sparky",{{0,0,1,1},{1,1,1,0}}->"S-pentomino",{{0,0,0,0,0,0,1,0,0,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0,0,0,0,0,0},{0,0,0,1,1,0,1,1,1,1,1,0,1,1,0,0,0,1,1,0,1,1,1,1,1,0,1,1,0,0,0},{0,1,0,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0,1,1,0,1,0},{1,0,0,0,1,0,1,0,0,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0,1},{0,0,0,0,1,1,1,0,0,0,0,0,1,1,0,0,0,1,1,0,0,0,0,0,1,1,1,0,0,0,0},{0,1,0,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,1,0},{0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0}}->"spider",{{1,1,0,0,0,0,1},{0,1,0,0,1,1,1},{0,1,0,1,0,0,0},{0,0,1,0,1,0,0},{0,0,0,1,0,1,0},{1,1,1,0,0,1,0},{1,0,0,0,0,1,1}}->"spiral",{{1,1,0,0,0,0,0,0},{0,0,0,0,1,1,0,0},{0,0,1,0,0,0,0,1},{0,0,1,0,0,0,0,1},{0,0,0,0,1,1,0,0},{1,1,0,0,0,0,0,0},{0,0,0,1,0,0,1,0},{0,0,0,1,0,0,1,0}}->"squaredance",{{0,0,1,1},{0,1,1,0},{1,1,0,0}}->"stairstep 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circle",{{0,0,0,0,1,0,0,0,0},{0,0,0,0,1,0,0,0,0},{0,0,0,0,1,0,0,0,0},{0,0,0,0,0,0,0,0,0},{1,1,1,0,0,0,1,1,1},{0,0,0,0,0,0,0,0,0},{0,0,0,0,1,0,0,0,0},{0,0,0,0,1,0,0,0,0},{0,0,0,0,1,0,0,0,0}}->"traffic lights",{{0,0,0,0,1,1},{0,0,0,0,0,1},{0,0,1,0,0,0},{0,0,1,1,0,0},{0,0,0,0,0,0},{1,1,1,1,0,0},{1,0,0,1,0,0}}->"trans-beacon on table",{{0,0,0,1,1},{0,0,1,0,1},{0,1,0,1,0},{0,1,0,0,0},{1,1,0,0,0}}->"trans-boat with tail",{{0,1,0,0,0,0},{1,0,1,0,0,0},{1,0,0,1,0,0},{0,1,1,0,1,0},{0,0,0,0,1,0},{0,0,0,0,1,1}}->"trans-loaf with tail",{{1,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,0,0,0,0,0,0,0,0,0,1,1},{0,1,1,0,0,0,0,0,0,0,0,0,1,1},{1,1,0,0,0,0,0,0,0,0,0,0,0,0}}->"transparent block reaction",{{1,1,0,0,0,0,0},{1,1,0,0,1,0,0},{0,0,1,1,0,1,0},{0,0,1,0,0,1,0},{0,1,0,0,0,1,1},{0,0,1,1,1,0,0},{0,0,0,0,1,0,0}}->"trice tongs",{{1,1,0,0,0,0},{1,0,1,0,0,0},{0,0,0,0,0,0},{0,0,1,0,1,0},{0,0,0,0,0,1},{0,0,0,0,1,1}}->"tripole",
{{0,1,0},{1,0,1},{0,1,0}}->"tub",{{0,0,0,0,1,0,1,0,0,0,0,0,0},{0,0,0,0,1,1,0,1,0,0,0,0,0},{0,0,0,0,0,0,0,1,1,1,0,0,0},{0,0,0,0,1,1,0,0,0,0,1,0,0},{1,1,0,1,0,0,1,1,0,0,1,0,0},{0,1,0,1,0,0,0,0,1,0,1,1,0},{1,0,0,0,1,0,0,0,1,0,0,0,1},{0,1,1,0,1,0,0,0,0,1,0,1,0},{0,0,1,0,0,1,1,0,0,1,0,1,1},{0,0,1,0,0,0,0,1,1,0,0,0,0},{0,0,0,1,1,1,0,0,0,0,0,0,0},{0,0,0,0,0,1,0,1,1,0,0,0,0},{0,0,0,0,0,0,1,0,1,0,0,0,0}}->"tubber",{{0,1,0,0,0},{1,0,1,0,0},{0,1,0,1,0},{0,0,0,1,0},{0,0,0,1,1}}->"tub with tail",{{0,1,1,0,1,1,0},{0,1,1,0,1,1,0},{0,0,1,0,1,0,0},{1,0,1,0,1,0,1},{1,0,1,0,1,0,1},{1,1,0,0,0,1,1}}->"tumbler",{{0,1,1,1,0,0,0,0,0,0,0,1,0,0},{0,1,1,0,0,1,0,1,1,0,1,1,0,0},{0,0,0,1,1,1,0,0,0,0,1,0,0,0},{0,1,0,0,1,0,1,0,0,0,1,0,0,0},{1,0,0,0,0,1,0,0,0,0,1,0,0,1},{1,0,0,0,0,1,0,0,0,0,1,0,0,1},{0,1,0,0,1,0,1,0,0,0,1,0,0,0},{0,0,0,1,1,1,0,0,0,0,1,0,0,0},{0,1,1,0,0,1,0,1,1,0,1,1,0,0},{0,1,1,1,0,0,0,0,0,0,0,1,0,0}}->"turtle",{{0,0,1,0,0,0,1,0,0},{0,1,0,1,0,1,0,1,0},{0,1,0,1,0,1,0,1,0},{1,1,0,1,0,1,0,1,1},{0,0,0,0,1,0,0,0,0}}->"twinhat",{{1,1,0,0,0,0,0,0,0},{0,1,0,0,0,0,0,0,0},{0,1,0,1,0,0,0,0,0},{0,0,1,1,0,0,0,0,0},{0,0,0,0,0,1,1,0,0},{0,0,0,0,0,1,0,1,0},{0,0,0,0,0,0,0,1,0},{0,0,0,0,0,0,0,1,1}}->"two eaters",{{0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0},{1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,0},{1,1,0,1,0,0,0,1,1,1,1,0,0,1,1,0,1,1,0,0,1,1},{0,0,0,0,1,0,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1},{1,1,0,1,0,0,0,1,1,1,1,0,0,1,1,0,1,1,0,0,1,1},{1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,0},{0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0}}->"two glider fuse",{{0,1,1,0,0,0,0,0},{0,1,1,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,1,0,0,0,0,0,0},{1,0,1,0,0,0,0,0},{1,0,0,1,0,0,1,1},{0,0,0,0,1,0,1,1},{0,0,1,1,0,0,0,0}}->"unix",{{1,0,1},{1,1,1}}->"U-pentomino",{{1,0,0},{1,0,0},{1,1,1}}->"V-pentomino",{{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0},{1,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1},{1,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0},{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}->"washer woman",{{0,0,0,0,0,0,0,0,0,0,1,1,0,1,1,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0},{0,0,0,0,0,1,1,1,0,1,0,0,1,1,1,0,0,1,1,1,1,0},{0,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,1,0,0,0,0,1},{1,0,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0,1,1,0},{1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0},{0,1,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}->"wasp",{{0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0},{1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,1},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0},{0,0,1,0,0,0,1,1,1,1,0,0,0,1,0,0},{0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0},{0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0},{0,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0}}->"weekender",{{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{1,0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0},{1,0,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0,0,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0,0,0},{1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0,0},{0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,0,0,1,0,1,0,0,0,1,1,0,0,0},{0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0,0,0,0,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0,0},{0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,1,1,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,0,0,1,1,0,1,0},{0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,1,0},{1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,1,0,1,0,1,1,0,1,1},{1,0,0,0,0,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0,1,0,1,0},{1,0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,1,1,0,0,0,0,1,0,0,1,0,1,0},{0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,1,1,0,0,0,0,1,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0}}->"wickstretcher",{{1,0,0},{1,1,0},{0,1,1}}->"W-pentomino",{{0,1,0},{1,1,1},{0,1,0}}->"X-pentomino",{{0,0,1,0},{1,1,1,1}}->"Y-pentomino",{{1,1,0},{0,1,0},{0,1,1}}->"Z-pentomino"};

Manipulate[ArrayPlot[If[av,Mean,Last]@CellularAutomaton[{224,{2,{{2,2,2},{2,1,2},{2,2,2}}},{1,1}},{conf,0},t+1,{{1,t+1},Automatic}],ImageSize->{370,370}],{{conf,{{0,1,0},{1,1,1},{0,1,0}},"configuration"},Evaluate@LifeConfigurations,ControlType->"PopupMenu"},{{t,0,"steps"},0,200,1},
{{av,False,"average all steps"},{True,False}},SaveDefinitions->True]

THIS NOTEBOOK IS THE SOURCE CODE FROM
"Game of Life Configurations" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/GameOfLifeConfigurations/
Contributed by: Eric Weisstein and Stephen Wolfram

Příklad: 2D automat simulující Bělousovovu-Žabotinského reakci

Manipulate[SeedRandom[seed];
ArrayPlot[CellularAutomaton[{1350851716507335422,{20,1},{1,1}},{Table[RandomInteger[{19},200],{i,1,200}],0},{{{steps}},All,All}],ImageSize->360,
ColorFunctionScaling->False],
{{steps,0},0,150,1,Appearance->"Labeled"},Delimiter,
{{seed,1,"new initial conditions"},1,10000,1,Appearance->"Labeled"}]

THIS NOTEBOOK IS THE SOURCE CODE FROM
"Idealized Belousov-Zhabotinsky Reaction" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/IdealizedBelousovZhabotinskyReaction/
Contributed by: Luca Zammataro

Cvičení

Předpokládejme, že chceme vybudovat železniční rychlodráhu spojující velká americká města s aspoň 500 000 obyvateli. Železniční síť musí být souvislá (existuje cesta mezi libovolnými dvěma městy) a koleje povedou mezi dvojicemi měst po nejkratších spojnicích (geodetikách). S ohledem na úsporu nákladů požadujeme, aby celková délka kolejí byla co nejmenší. Které dvojice měst máme spojit, abychom splnili tyto požadavky? Znázorněte mapu USA s vyznačenými městy a železniční sítí. Jaká bude celková délka kolejí?

Návod:

Použijte databázi CityData k nalezení všech měst v USA, které mají aspoň 500 000 obyvatel.

Zkonstruujte neorientovaný graf, jehož vrcholy jsou města. Mezi každými dvěma městy povede hrana, jejíž délku stanovíte pomocí GeoDistance. (Ke konstrukci grafu s ohodnocenými hranami použijte volbu EdgeWeight.)

Pomocí FindSpanningTree najděte minimální kostru grafu, hrany této kostry můžete získat pomocí EdgeList.

Pomocí GeoGraphics vykreslete mapu USA společně s hranami grafu tvořícími minimální kostru (použijte GeoPath).

Vypočítejte celkovou délku kolejí jako součet délek příslušných hran.