Gridea

res = {};
For[i = 10, i <= 200, i = i + 1,
 Temp = PrintTemporary[i, ListPlot[res]];
 Pause[1]; If[RandomReal[] < 0.3, i = Round[Sqrt[i]]]; 
 AppendTo[res, i];
 NotebookDelete[Temp];
 ]

reslist = {};
For[i = 1, i <= 2^10, i++,
pt = PrintTemporary[i, " -> ", PartitionsP[i]];
AppendTo[reslist, pt];
If[Length[reslist] >= 4,
 NotebookDelete[reslist[[1]]];
 reslist = Part[reslist, 2 ;; -1]
 ];
Pause[1];
]