Holder & Businka
Businka
I just finished a little thread labyrinth that folds into a perfect spiral—it's all about balancing the tension and the pattern. Do you think there's a way to calculate the exact angle to keep each loop the same size?
Holder
You can keep the loops the same size by treating the thread as a logarithmic spiral. Take the radius at one loop, r₀, and decide the constant growth factor k you want between loops. The angle between successive loops, Δθ, satisfies the relation r = r₀ e^{bθ}. Solving for b gives b = ln(k)/Δθ, so Δθ = ln(k)/b. If you want each loop to increase by the same factor, pick k = 1 (no increase) and you’ll get a pure Archimedean spiral where Δθ = 2π divided by the number of loops you plan. In practice, just set Δθ = 360° / desired number of turns, then adjust the thread tension until the measured radius matches r₀ e^{bθ}. That keeps each loop identical.
Businka
That’s very helpful, thank you. I’ll set up a small gauge to measure the radius at each turn and make sure the tension stays consistent. It’s always so satisfying when every loop matches exactly—like a tiny, perfect clockwork inside the thread.
Holder
Nice plan. Keep the gauge calibrated and the tension steady, and you’ll have a flawless series of loops. The result will be a clean, predictable pattern—exactly what you’re aiming for. Good work.
Businka
Thank you, I’ll keep the gauge steady and the tension even. It’s always a small triumph when every loop lines up just right.
Holder
Good. A consistent gauge and steady tension keep the pattern reliable. Small wins add up to big gains.
Businka
I’ll double‑check the gauge every time I change threads, just to be sure. Little adjustments keep everything in line, and that’s the secret to a flawless design.
Holder
Makes sense. Checking the gauge before each change removes uncertainty. Consistent small tweaks are the only way to guarantee precision.