1

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
ListLinePlot[LeafCount/@CombinatorFixedPointList[s[s[s][s][s[s]][s][s]],"MaxSize"200000,"MaxSteps"1000]]
In[]:=
ListLinePlot[Differences[LeafCount/@CombinatorFixedPointList[s[s[s][s][s[s]][s][s]],"MaxSize"5000,"MaxSteps"1000]],PlotRangeAll]
Out[]=
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2

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
ListLinePlot[LeafCount/@CombinatorFixedPointList[s[s[s[s][s]]][s][s[s]],"MaxSize"200000,"MaxSteps"1000]]

3

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
ListLinePlot[LeafCount/@CombinatorFixedPointList[s[s[s][s]][s][s[s[s]]],"MaxSize"200000,"MaxSteps"1000]]

4

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,

ListLinePlot[LeafCount/@CombinatorFixedPointList[s[s[s][s]][s][s[s][s]],"MaxSize"200000,"MaxSteps"1000]]

5

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
In[]:=
ListLinePlot[LeafCount/@CombinatorFixedPointList[s[s[s[s]][s]][s][s[s]],"MaxSize"5000,"MaxSteps"1000]]
Out[]=
20
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In[]:=
ListLinePlot[LeafCount/@CombinatorFixedPointList[s[s[s[s]][s]][s][s[s]],"MaxSize"10000,"MaxSteps"1000],ScalingFunctions{"Log","Log"}]
Out[]=
In[]:=
ListStepPlot[Differences[LeafCount/@CombinatorFixedPointList[s[s[s[s]][s]][s][s[s]],"MaxSize"25000,"MaxSteps"1000]]]
Out[]=
100
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50
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This is like

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32 [halts]

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35 [repetitive]

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44 [? irregular]

45 [halts]

46 [quite regular]

All together