User blog comment:LittlePeng9/Color reducing for Turing machines/@comment-10429372-20140426114729

Some improvements:

\rfloor \text{log}_2(n) +1 \lfloor can be improved to \rceil \text{log}_2(n) \lceil. It greatly reduces the number of new states in case there are 2n colors.

For 3 colors, it it also possible with 6 states rather than 7:

When we read a 1 in the first cell, it can only be 1_. So we don't need an additional reading state.

When the 2 changes to a space we only need five states!