For samosa
For samosa
In[]:=
obj=WolframModel[{{1,2,3},{4,5,6},{1,4}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{13,8},{7,10},{9,12},{11,14}},{{0,0},{0,0},{0,0},{0,0,0},{0,0,0}},10];
In[]:=
vols=MeanAround/@TransposeValues[obj["FinalState"],All,Automatic];
In[]:=
ListLinePlotTable[(Log[vols[[r+1]]]-Log[vols[[r]]])/(Log[r+1]-Log[r]),{r,Length[vols]-1}],
Out[]=
Need to look also away from corners.....
“Start from a node in the center of the triangular face”
For Sierpinski
For Sierpinski
In[]:=
obj=WolframModel[{{1,2,3}}{{1,4,6},{2,5,4},{3,6,5}},{{0,0,0}},8]
Out[]=
In[]:=
vols=MeanAround/@TransposeValues[obj["FinalState"],All,Automatic]
Out[]=
In[]:=
ListLinePlotTable[(Log[vols[[r+1]]]-Log[vols[[r]]])/(Log[r+1]-Log[r]),{r,Length[vols]-1}],
Out[]=
Other rule
Other rule
In[]:=
obj=WolframModel[{{{1,2},{2,3}}{{1,5},{5,2},{5,3},{2,1}}},{{1,2},{2,3}},13]
Out[]=
In[]:=
vols=MeanAround/@TransposeValues[obj["FinalState"],All,Automatic];
In[]:=
ListLinePlotTable[(Log[vols[[r+1]]]-Log[vols[[r]]])/(Log[r+1]-Log[r]),{r,Length[vols]-1}],
Out[]=
In[]:=
obj=WolframModel[{{{1,2},{2,3}}{{1,5},{5,2},{5,3},{2,1}}},{{1,2},{2,3}},14]
Out[]=
In[]:=
vols=MeanAround/@TransposeValues[obj["FinalState"],All,Automatic];
In[]:=
ListLinePlotTable[(Log[vols[[r+1]]]-Log[vols[[r]]])/(Log[r+1]-Log[r]),{r,Length[vols]-1}],
Out[]=
In[]:=
vols=%302;
In[]:=
Table[(Log[vols[[r+1]]]-Log[vols[[r]]])/(Log[r+1]-Log[r]),{r,Length[vols]-1}]
Out[]=
Perhaps 2.66
Frilled space
Frilled space
From the first section
From the first section
Grid graphs [[ things to understand here! ]]
Grid graphs [[ things to understand here! ]]
[[ Look at results for some triangulated surfaces ]]
[[ Look at results for some triangulated surfaces ]]
?? Color a surface by its local inferred curvature
Can be “Ricci flat” through a tradeoff of curvature and dimension......
Compare properties with triangulated surfaces.....
Compare properties with triangulated surfaces.....
Comparison with manifold case
Comparison with manifold case
Topological Characterization
Topological Characterization
https://demonstrations.wolfram.com/SimplicialHomologyOfTheAlphaComplex/
https://demonstrations.wolfram.com/SimplicialHomologyOfTheAlphaComplex/
Look at cycles in the graph
Look at cycles in the graph
Look at geodesics in the graph
Look at geodesics in the graph