User blog comment:Edwin Shade/Turing Machines and a Problem by Vel! Posed Half a Decade Ago/@comment-1605058-20171010173654/@comment-32876686-20171024014146

@LittlePeng9

I've got an idea then.

How about a type of Turing Machine whose tape contains a set of cells, each one of them representing another TM with a prescribed set of rules. These mini-TM's are to be considered changing in that their rules may be altered according to the rules of the big-TM. Thus you end up with the tape at successive intervals of time containing different arrangements of Turing Machines.

I haven't worked out what might happen after than, but I know such a machine is well-definable. I could also make a machine that has a tape containing a set of big-TM's, and then I could have a higher level TM for the ruleset of this TM, and so on. I could diagnolize over this and make a function which is hopefully more powerful than the normal BB(n) function.