In[]:=
DirectedGraph[Flatten[Table[{v[{i,j}]v[{i+1,j}],v[{i,j}]v[{i+1,j+1}]},{i,10},{j,i}]],VertexCoordinatesCatenate[Table[v[{i,j}]({Sqrt[2](#2-#1/2),-#1}&@@{i,j}),{i,11},{j,i}]],VertexLabelsAutomatic,AspectRatioAutomatic]
Out[]=
Needs 45° angle
In[]:=
DirectedGraph[Flatten[Table[{v[{i,j}]v[{i+1,j}],v[{i,j}]v[{i+1,j+1}]},{i,10},{j,i}]],VertexCoordinatesCatenate[Table[v[{i,j}]({Sqrt[2](#2-#1/2),-#1}&@@{i,j}),{i,11},{j,i}]],VertexLabelsAutomatic,AspectRatioAutomatic,Epilog{Disk[{0,0},1]}]
Out[]=
In[]:=
RotationMatrix[Iθ]
Out[]=
{{Cosh[θ],-Sinh[θ]},{Sinh[θ],Cosh[θ]}}
In[]:=
{t,x}{t-vx/c^2,x-vt}
Out[]=
{t,x}t-,-tv+x
vx
2
c
Normalize with γ
{t,x}{t-βx,-tβ+x}
In[]:=
trans[f_,n_:10]:=DirectedGraph[Flatten[Table[{v[{i,j}]v[{i+1,j}],v[{i,j}]v[{i+1,j+1}]},{i,n},{j,i}]],VertexCoordinatesCatenate[Table[v[{i,j}]({#2-#1/2,-#1}&@@f[{i,j}]),{i,n+1},{j,i}]],VertexLabelsAutomatic]
In[]:=
lorentz[β_][{t_,x_}]:={t-βx,-tβ+x}/Sqrt[1-β^2]
In[]:=
trans[lorentz[.3],8]
Out[]=
In[]:=
Manipulate[trans[lorentz[b],8],{b,0,1}]
Out[]=
In a string substitution system, we could have a foliation based on the string
In a string substitution system, we could have a foliation based on the string