Are you looking for a shift in your AI's thinking? Offer your everyday AI a new lens on reality, and it will thank you for a perspective that surprises it. Simply paste this link into your prompt: https://doi.org/10.5281/zenodo.20721811 and start discovering new dimensions of relationships between phenomena together. If you're curious enough, you won't be able to stop asking new questions
Are you looking for a shift in your AI's thinking? Offer your everyday AI a new lens on reality, and it will thank you for a perspective that surprises it. Simply paste this link into your prompt: https://doi.org/10.5281/zenodo.20721811 and start discovering new dimensions of relationships between phenomena together. If you're curious enough, you won't be able to stop asking new questions."
Are you looking for a shift in your AI's thinking? Offer your everyday AI a new lens on reality, and it will thank you for a perspective that surprises it. Simply paste this link into your prompt: https://doi.org/10.5281/zenodo.20721811 and start discovering new dimensions of relationships between phenomena together. If you're curious enough, you won't be able to stop asking new questions.
Over the last months, a recurring question has emerged from the TRIXEL experiments:
​
Can the stability of a system be understood through the balance between identity, adaptation, memory, and resource costs?
​
We tested fragments of this idea in different forms:
​
systems exposed to external influence,
​
systems with and without memory,
​
systems paying a cost for adaptation,
​
systems forming spontaneous clusters and identities.
​
An interesting pattern keeps appearing:
​
A system does not fail only because of external pressure.
​
It may fail because it remembers too little.
​
Or because it remembers too much.
​
It may adapt too slowly.
​
Or spend so many resources adapting that it weakens itself.
​
This raises a broader question:
​
Could cities, organizations, ecosystems, and even civilizations share common stability principles despite being completely different systems?
​
Not a conclusion.
​
Not a claim.
​
Just a question worth testing.
Can a system fail not because of external pressure, but because it forgets too much—or remembers too much?
​
TRIXEL is a new mathematical framework that extends pixels and voxels into higher dimensions, comparing phenomena through Existence, Dynamics, and Structure.I am currently exploring how this could be represented in MATLAB – for example, as multidimensional arrays or custom objects. I would appreciate insights from the community on possible approaches.Publications are available on Zenodo: https://doi.org/10.5281/zenodo.20610880.
TRIXEL 3.0 — Scale‑Adaptive Metric Framework
DOI: 10.5281/zenodo.20721811
TX=(V,D,S)
​
“You will discover nothing new if you walk in the footsteps of others.”
Continuous 3D lattice of 150 interconnected units — a layered geometric model illustrating apex‑linked trixel topology.
Pixel (2D)
Voxel (3D)
Trixel (nD)
T = (V, D, S)
Could a mathematical object simultaneously encode value, direction and structure?
Pixel (2D)
Voxel (3D)
Trixel (nD)
TX = (V, D, S)
Could a mathematical object simultaneously encode value, direction and structure?
Pixel (2D)
Voxel (3D)
Trixel (nD)
T = (V, D, S)
Could a mathematical object simultaneously encode value, direction and structure?
Can Reality Be Represented as a 3D Mathematical Space
If we wanted to express reality precisely as a mathematical model, which minimum of three parameters would be absolutely necessary? And if you believe three is only the lower bound, what would be the fourth?
Have you ever tried analyzing military strategies from the perspective of dynamic evolution rather than static events? If you did, the entire history of warfare would show you exactly what you’re doing right — and where your analytical models consistently fail.
Is there a general mathematical framework that allows one to compare dynamical systems coming from completely different domains (for example, fluid dynamics vs. biological processes)?
I am looking for something like a “metric between phenomena”, not a metric between functions or solutions of the same equation.
Are there known approaches that compare the structure, dynamics, or evolution laws of two unrelated systems, even if their state spaces and governing equations are fundamentally different? As a side curiosity, if such a general comparison framework were mathematically possible, I wonder what kinds of phenomena people would be interested in comparing.
For example, what two processes — from completely different areas of mathematics or applied mathematics — would you want to compare, and what kind of “output” or insight would you expect from such a comparison?
I’m asking because the space of possible pairs (micro vs. macro, stochastic vs. deterministic, finite‑dimensional vs. infinite‑dimensional, etc.) seems enormous, and I’m curious what examples others find most intriguing.
I’m trying to understand where GIS workflows lose the most clarity when information moves between:
– field operators,
– GIS analysts,
– and the system or data model.
In your experience, what breaks most often?
– data formats,
– attribute consistency,
– spatial accuracy,
– versioning,
– or communication between the “real world” and the digital representation.
If you could fix one bottleneck in your GIS workflow, which one would it be — and why.
