Continuum Limit

In[]:=
NestGraphTagged[n|->{2n,n+1},0,10]
Out[]=
Infinite number of branches ; branching infinitely often
In[]:=
AdjacencyMatrix
//MatrixPlot
Out[]=

For us, the ordering of nodes is not arbitrary ; they are specific numbers....

In[]:=
NestGraph[n|->{2n,n+1},Range[0,1,1/10],4]
Out[]=
In[]:=
VertexList[%]
Out[]=
0,1,
1
10
,
1
5
,
11
10
,
2
5
,
6
5
,
3
10
,
3
5
,
13
10
,
4
5
,
7
5
,
1
2
,
3
2
,
8
5
,
7
10
,
17
10
,
9
5
,
9
10
,
19
10
,2,
21
10
,
11
5
,
12
5
,
23
10
,
13
5
,
14
5
,
5
2
,3,
16
5
,
27
10
,
17
5
,
18
5
,
29
10
,
19
5
,4,
31
10
,
21
5
,
22
5
,
33
10
,
23
5
,
24
5
,
7
2
,5,
26
5
,
37
10
,
27
5
,
28
5
,
39
10
,
29
5
,6,
32
5
,
34
5
,
36
5
,
38
5
,8,
41
10
,
31
5
,
43
10
,
33
5
,
9
2
,7,
47
10
,
37
5
,
49
10
,
39
5
,
42
5
,
44
5
,
46
5
,
48
5
,10,
52
5
,
54
5
,
56
5
,
58
5
,12,
64
5
,
68
5
,
41
5
,
72
5
,
43
5
,
76
5
,9,16
In[]:=
Histogram[%]
Out[]=
In[]:=
graphon2[x_,y_]:=1-Max[x,y]
In[]:=
NestGraphTagged[n|->{2n,n+1},Range[0,1,1/20],4]
Out[]=
In[]:=
NestGraphTagged[n|->{2n,n+1},Range[0,1,1/25],4]
Out[]=
In[]:=
NestGraphTagged[n|->{n+1,n+2},Range[0,1,1/25],4]
Out[]=

Analogies

Stochastic calculus

Binomial trees for e.g. pricing

Path integrals