In[]:=
GridGraph[{30,30}]
Out[]=
In[]:=
Graphics[HilbertCurve[4]]
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AdjacencyMatrix[GridGraph[{30,30}]]//MatrixPlot
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In[]:=
Map[Mean[Flatten[#]]&,Partition[AdjacencyMatrix[GridGraph[{30,30}]],{100,100}],{2}]//MatrixPlot
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In[]:=
rarray=RandomInteger[1,{50,50}];
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ArrayPlot[rarray]
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Times@@Dimensions[rarray]
Out[]=
2500
In[]:=
Map[Mean[Flatten[#]]&,Partition[rarray,{10,10}],{2}];
In[]:=
Times@@Dimensions[%15]
Out[]=
25
In[]:=
ArrayPlot[%15]
Out[]=
In[]:=
HilbertCurve[6]
Out[]=
Line{{0,0},{1,0},{1,1},{0,1},{0,2},{0,3},{1,3},{1,2},{2,2},{2,3},{3,3},{3,2},{3,1},{2,1},{2,0},{3,0},{4,0},{4,1},{5,1},{5,0},{6,0},{7,0},{7,1},{6,1},
⋯4049⋯
,{56,1},{56,0},{57,0},{58,0},{58,1},{59,1},{59,0},{60,0},{61,0},{61,1},{60,1},{60,2},{60,3},{61,3},{61,2},{62,2},{62,3},{63,3},{63,2},{63,1},{62,1},{62,0},{63,0}}
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In[]:=
Length[First[HilbertCurve[6]]]
Out[]=
4096
Sample according to Hilbert curve
First[HilbertCurve[6]]+1