pulled out my old Wolfram Summer School NKS summer school project from 2008. (i was so young then! hahaha!)

"Project: perturbing turing machines
a.k.a terpurbing gurint sachinem

Vermont, Summer 2008

Background

And the reason this is important is that in any real experiment, there are inevitably perturbations on the system one is looking at

— Stephen Wolfram, A New Kind of Science, p. 324

Perturbations to Elementary Cellular Automata (ECAs) have been studied extensively. Under moderate noise, ECA patterns often sustain only local changes, eventually recovering globally. More complicated ECA rules exhibit bigger disturbances but retain some tolerance to noise.

Here, we attempt a parallel exploration on Turing Machines (TMs). The question: Do Turing Machines exhibit similar resilience to single-step perturbations?"

With OpenAI o1 model and Wolfram Language I can do a much richer exploration in half a day in 2025 than i could do in a week in 2008. Arguably I'm a much better computational thinker 17 years later, but the tools really do make a lot of the difference.

Most the work I did today was to figure out the best way to convert my old poster presentation and older code into a useful prompt for Wolfram LLM Assistant and OpenAI o1 to understand the full scope of my investigation. Once I got that right the code the computer generated mostly "just worked" with very minor final touches by me. Remarkable.

These are very non-trivial concepts I am playing with and Wolfram Language when you are working on abstract things like Turing Machines isn't easy for an LLM.

I am delighted by todays effort. and I might even really finish this all the way to publishing it, since I never did that in 2008.

code to be added eventually once I finish this into a nice notebook.

for now, some screengrabs.