# Repeated multiplying x2

is it possible to have 1 blue, then 1 red, then 2 blue and 2 red, then 4 blue and 4 red, 8, 16, etc… i have a setup (probably not optimized) that can do 1 1 2 2 4

iv’e tried a few things with the next 4 but i could only get 4 3.

The Turing Tumble can only do finite length patterns, or repeating patterns of a bounded length… so while you could perhaps start outputting 1,1,2,2,4,4,… , at some point the growth of the pattern would have to stop, and it would either terminate (at an interceptor), or start over again 1,1,2,2,… For example, it might be possible to do 1,1,2,2,4,4,8,8,1,1,2,2,4,4,8,8,1,1,2,2,…

How much of the doubling sequence you could produce will depend on the size of the board. It sounds like you’ve gotten quite close to 1,1,2,2,4,4, (stop, or repeat). I’m doubtful that you could get up to 1,1,2,2,4,4,8,8.

BRBBRRBBBBRRRRBBBBBBBBRRRR - This is a suitable task for solver.
This is the maximum that my Python solver allows. He goes through 14 billion combinations for 7 bits in 1 hour and 20 minutes. When switching to 8 bits, it will be 81 times longer. It’s too long.