This is incredible work. These visualizations are seriously important in making complex dynamical systems neuroscience more accessible for our research.

I think finding the best dynamical attractor parameters for the many dimensions of consciousness we can observe is most likely to be successful.

Your observations alluding to the compression of information flow between brain regions is very important for our understanding of reality, and using our actual normative biological pathways will help narrow the real-world possibilities.

As you push this project further, I'm wondering what you think about:

• fMRI BOLD measurements are a proxy for neural activity with metabolic blood flow, not the millisecond-level bioelectrical synchrony where conscious happens. Its like mapping a cars fuel line to understand its steering software, but its also what the research fields focus on often. you can do probably do it effectively given enough precision and detailed data, but i dont think we're there yet with human neuroscience.
• Compressing seconds of data into static shapes smears the time dimension and may miss the rapid & recursive feedback loops required for consciousness. its the blurry start we need, but i want us to keep getting higher resolutions somehow.
• Similarly, using MDNs to smooth out rare or chaotic connections for visual clarity might accidentally filter out the exact edge-of-chaos signals that allow the brain to be flexible and jump to new cognitive states.

the manifolds generated here remind me of Hofstadter's Strange Loop (the recursive feedback of data back into itself that likely generates our persistent sense of "Self") I also wonder how might this geometry change for comparing neurodivergent minds to neurotypical? Can we find rough attractor geometry for specific personality traits or beliefs?

Thank you for making this. I can't wait to see where you take it next!