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ADM-like formalism
ADM-like formalism
Given a spacetime lattice, this generates an ordering of how to hit points in the lattice.
In the continuum, any angle of slicing will work.
In[]:=
rlist=RandomInteger[{-1,1},20]
Out[]=
{-1,0,1,-1,1,1,0,0,1,0,1,1,-1,0,0,1,-1,1,1,0}
In[]:=
Flatten[Table[{x,y+rlist[[x]]},{y,20},{x,20}],1];
In[]:=
Graphics[{Line[%],Style[Point[#],Red]&/@%}]
Out[]=
In[]:=
Table[Floor[.34n],{n,20}]
Out[]=
{0,0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6}
In[]:=
pts=With[{rlist=Table[Floor[.34n],{n,20}]},Flatten[Table[{x,y-rlist[[x]]},{y,20},{x,20}],1]];
In[]:=
Graphics[{PointSize[.02],Line[pts],Style[Point[#],Red]&/@pts}]
Out[]=
In[]:=
Graphics[{PointSize[.02],Style[Table[Point[{x,y}],{x,20},{y,20}],Blue],Line[pts],Style[Point[#],Red]&/@pts}]
Out[]=
In[]:=
pts=With[{rlist=Table[Floor[.34n],{n,8}]},Flatten[Table[{x,y-rlist[[x]]},{y,8},{x,8}],1]]
Out[]=
In[]:=
SortBy[%,Last]
Out[]=
In[]:=
First/@%
Out[]=
{6,7,8,3,4,5,6,7,8,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,1,2,3,4,5,1,2}
This gives an analog of relativistic transformations for sequential CAs.