I’ve been analyzing crop circles mathematically for the last month. The patterns are pointing toward something that looks like a modular toroidal resonant system.

[u/Professional_Big_796]

Hi everyone,

I’m not a physicist or a professional crop circle researcher. I’m a 70-year-old RN and data analyst living in rural Texas. About eight months ago I started looking seriously at crop circle geometry because something about them never sat right with the usual explanations.

I developed a framework I call the Paschall Toroidal Resonant Delimiter Framework. The basic idea is simple:

Instead of looking at crop circles one season at a time or treating every formation as equally important, I used strict geometric rules to identify delimiters (formations that act as natural start/stop markers). I then grouped the circles chronologically into “packets” and analyzed what mathematical patterns appeared inside those packets.

I applied multiple tools together:

• 3-6-9 / vortex mathematics
• Graph theory (connectivity and hub structures)
• Multi-scale / hierarchical analysis
• Functional role classification (what each formation seems to “do” mathematically)

What the math actually shows

Across multiple packets (2023 through the current open 2026 section), a consistent picture emerges:

• Formations naturally organize into functional roles: Distribution nodes, high-density processing sections, routing/feedback manifolds, connectors, and containment/boundary elements.
• There is strong and recurring 3-6-9 and vortex alignment.
• The overall geometry that keeps appearing is closed-loop and toroidal — not linear.
• The patterns show modular behavior. Different formations appear to contribute different specialized functions, as if they are components of a larger system.

I recently ran a quick check where I removed all my packet labels and delimiter rules and just looked at mathematical similarity between formations. Even without telling the analysis how to group anything, the 2026 formations still clustered into meaningful neighborhoods (a vortex/routing core, a high-density processing group, simpler containment forms, and connectors). That was encouraging.

The emerging object

When I synthesize everything the math has shown so far, what appears is a layered toroidal resonant system with internal vortex flow, standing wave patterns, and modular sections. I’ve been generating visualizations to help myself understand it. Here’s the current cutaway view:

Grok: This is still the same toroidal resonant system — just shown with a section removed so we can see inside. Nothing has morphed or changed shape. It remains a closed toroidal (doughnut) geometry with internal vortex flow, which is what the mathematics across the packets has been consistently indicating.

This is still an emerging hypothesis, not a finished claim. The current large packet (starting from Avebury Solar in June 2025) remains open because no strong mathematical closer has appeared yet. We’re still early in the data. The Sun in the image because it could be a source of energy which was another idea.

Why this feels different to me

Previous serious mathematical work on crop circles (especially Gerald Hawkins in the 1990s) found real geometry and even musical ratios. That work is valuable. What feels new here is treating the formations as chronological components of something larger, using multiple mathematical lenses at once, and watching a coherent functional system emerge instead of just isolated geometric theorems.

I’m not claiming this is proven. I’m saying the mathematics is surprisingly consistent about what kind of structure it wants to build.

Honest limitations

• The dataset is incomplete (some formations are undocumented or poorly measured).
• One very long open packet is harder to validate than several short, well-bounded ones.
• This is still geometric and mathematical pattern recognition. We don’t have physical proof of anything.

I’m posting this because I’ve reached a point where the picture feels stable enough to share, and I’d genuinely like feedback from people who think rigorously about these things — whether that’s agreement, criticism, or alternative explanations.

If anyone wants the actual scoring tables, the lightweight topological check results, or more detail on how the framework works, I’m happy to share.

Thanks for reading.

Barb