I've been exploring a simple, discrete formula as a potential meta-pattern across scales in nature:

ϕ:=Ω−Ω/2 with Ω←Ω+1 where Ω is an integer counter.

To test it, I looked for characteristic length ratios in various systems. The results are intriguing:

Bacterial Vortices: Spacing between vortices (~25µm) / cell length (~5µm) = 5.

Ocean Eddies: Eddy radius (~120km) / Rossby radius (~50km) ≈ 2.4 (very close to 2.5). The formula gives φ=2.5 at Ω=5.

Jupiter's Great Red Spot: Long axis (24k km) / short axis (12k km) = 2.

Turbulence: The famous energy spectrum slope is -5/3 (≈1.666). The formula gives this at a fractional state Ω=10/3.

The pattern suggests that stable structures across scales tend to "lock in" to simple integer or half-integer ratios. It feels like a signature of discrete, information-theoretic organization underlying physical phenomena.

I'm not a professional physicist. I'm an autodidact and entrepreneur who has been thinking about this for a long time. I'm sharing this here to get feedback from this community.

Is this just a case of cherry-picking and numerology? Or could it point to a deeper principle? What other systems or datasets should I look at to test or break this idea?

More details and visuals are in this Twitter thread: https://x.com/qiox178191/status/1965440143504154896