3n+1

cyc[n_Integer, m_Integer] :=
 Max@Table[
   NestWhileList[
     If[OddQ[#], 3 # + 1, #/2] &,
     i,
     # != 1 &
     ] // Length,
   {i, n, m}
   ]

ArrayPlot[
 Table[
  cyc[x, y],
  {x, 1, 6},
  {y, 1, 6}
  ],
 ColorFunction -> "GreenPinkTones"]