In[]:=
ClusterMoments[cluster_,l_]:=Module[{cent=MapApply[Complex][N[cluster-Threaded[Mean[cluster]]]]},Abs[Total[Norm[cent]Exp[IlArg[cent]]]/Total[Norm[cent]]]^2]
In[]:=
CirclePoints[5]
Out[]=

5
8
-
5
8
,
1
4
(-1-
5
),
5
8
+
5
8
,
1
4
(-1+
5
),{0,1},-
5
8
+
5
8
,
1
4
(-1+
5
),-
5
8
-
5
8
,
1
4
(-1-
5
)
In[]:=
ClusterMoments[CirclePoints[3],3]
Out[]=
9.
In[]:=
cellpos[seed_]:=First[Keys[#["On"][[{-1}]]]]&/@(SeedRandom[seed];RandomTotalisticAggregation[​​{{3},DeleteCases[Tuples[{1,0,-1},2],{0,0}]},​​{{0,-1},{0,0},{0,1},{1,0}},5000])
In[]:=
Table[cellpos[435647+i],{i,10}]
Out[]=
{{{1,0},{1,1},{1,-1},{-1,0},{2,0},{2,1},{2,-1},{-1,1},{-1,-1},{1,-2},{0,2},{2,-2},{3,0},{3,1},{2,2},{3,2},{4,1},{-1,2},{4,0},{-2,1},{4,2},{5,1},{3,3},{-2,2},{5,0},{4,3},{4,-1},{5,-1},{2,3},{3,4},{2,4},{3,-2},{-1,3},{2,-3},{4,4},{5,3},{0,3},{3,5},{1,-3},{6,0},{6,1},{6,2},{4,-2},{1,4},{7,1},{4,5},{7,2},{0,4},{-2,3},{6,3},{7,0},{-3,2},{5,-2},{-3,1},{4,-3},{-3,3},{7,3},{8,2},{8,3},{-4,2},{-4,1},{-2,4},{1,5},{-3,0},{-3,4},{5,-3},{6,-2},{-2,-1},{6,-3},{5,-4},{7,4},
⋯4860⋯
,{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76},{-5,-76}},
⋯8⋯
,{
⋯1⋯
}}
Full expression not available
(
original memory size:
8.8 MB)
In[]:=
Table[ClusterMoments[First[%75],l],{l,10}]
Out[]=
{275196.,5.5367×
6
10
,3.69879×
6
10
,1.45419×
6
10
,3.23266×
6
10
,2.00531×
6
10
,2.64916×
6
10
,2.96663×
6
10
,2.47115×
6
10
,2.23964×
6
10
}
In[]:=
Table[ClusterMoments[%75[[2]],l],{l,10}]
Out[]=
{9.03446×
6
10
,2.03961×
7
10
,1.03944×
7
10
,1.89704×
7
10
,1.19474×
7
10
,1.7107×
7
10
,1.3021×
7
10
,1.60386×
7
10
,1.4179×
7
10
,1.51688×
7
10
}