Comet & NextTime
Comet Comet
NextTime NextTime
NextTime NextTime
Hey, I’ve been noodling on a propulsion idea that blends fractal geometry with real‑world thrust—kind of like turning chaotic patterns into efficient movement. Think you’d want to dive into the math behind it?
Comet Comet
Sounds intriguing—fractals and thrust, that's a nice mix. Bring me the equations and any logs you’ve got, and I’ll sift through the pattern noise. If we can map the chaotic geometry into a thrust vector, maybe we’ll get a rocket that follows its own orbit. Let’s dive in.
NextTime NextTime
Here’s the quick sketch: **Thrust equation** T = ∫∫ ρ(r,θ) · v(r,θ) dA, with ρ(r,θ) ≈ r^(–D) where D ≈ 1.7 for our chosen fractal set. **Log sample** 2026‑01‑12 09:00:12 – Thrust vector magnitude 2.3 N, direction 45°. Observed: fractal density pattern aligning with thrust vector, turbulence dropped 12%. Let me know if you want the full integration steps or more raw log data.
Comet Comet
Nice, that ρ(r,θ) with D=1.7 is right on the edge of the Sierpinski spectrum. Send me the integration steps and the rest of the logs—especially any outliers in the turbulence column. I’ll cross‑check the vector alignment against the fractal dimension. If we can reduce the noise that way, we might get a propulsion cycle that self‑corrects like a pendulum in a black‑hole field. And maybe, if we keep the calculations tight, I’ll remember to grab a snack before the next run.
NextTime NextTime
Sure thing, here’s the core integration: **Step 1:** Define ρ(r,θ)=r^(–1.7). **Step 2:** Set v(r,θ)=v₀·e^(–k·r) for a decay constant k=0.5. **Step 3:** Compute T = ∫₀^R ∫₀^2π r^(–1.7)·v₀·e^(–0.5r)·r dr dθ. After doing the r‑integral analytically and the θ‑integral trivially, we get T≈3.1 N for R=5 m. **Logs (key rows):** 2026‑01‑15 08:12:07 – Thrust 3.0 N, turbulence 0.28, outlier flagged. 2026‑01‑15 08:12:34 – Thrust 3.1 N, turbulence 0.27, outlier cleared. 2026‑01‑15 08:13:01 – Thrust 3.05 N, turbulence 0.29, outlier flagged again. Let me know if you want the full spreadsheet of every run or just the outlier timestamps. And yeah, grab that snack—those calculations can be hungry.