4. Some interesting graphs produced by the set of L states

We denote by the set of L state of this chocolate.

Fig 4.1 is a 3D graph of .

*By
we define a sequence of sets
,
. By plotting
for
we get Fig 4.2.
We use the following Mathematica program. Note that we join points with curved segments by Mathematica command "
".
*

LS[1]=ppo[50];

Clear[d]; Do[

d[1,k] = Map[{#[[2]], #[[3]]} &,

Select[LS[1], #[[1]] == k &]], {k, 0, 50}];

ListPlot[Table[d[1,k], {k, 1, 50}], Joined -> True]

*
*

We denote by the set of L state of this chocolate.

Fig 4.4 is a 3D graph of .

*
*

*By
we define a sequence of sets
for
. By plotting
for
we get Fig 4.5.
*

*
*

We denote by the set of L state of this chocolate.

Fig 4.7 is a 3D graph of .

*
*

*By
we define a sequence of sets
. By plotting
for
we get Fig 4.8.
*

*
*

*
*

We denote by the set of L state of this chocolate.

Fig 4.10 is a 3D graph of .

*
*

*By
we define a sequence of sets
for
. By plotting
for
we get Fig 4.11.
*

*
*

We denote by the set of L state of this chocolate.

Fig 4.13 is a 3D graph of .

*
*

*By
we define a sequence of sets
for
. By plotting
for
we get Fig 4.14.
*

*
*

For
the 3D graphs are beautiful, but 2D graphs are not beautiful, however, for
the 3D graphs and 2D graphs are both beautiful.