Begin with an Archimedean spiral
For a model with a constant radial increase per full turn, use r(θ) = a + bθ. Here r is the distance from the centre, θ is the angle in radians, a is the starting radius, and b controls how quickly the curve moves outward.
One full turn adds 2π radians. If the spacing between successive turns of the centreline is s, then b = s / (2π). For N turns, the final angle is T = 2πN and the final centreline radius is a + sN.
Starting radius a = 5 mm. Illustrative strand width = 3 mm. Diagram scales to fit; use the numbers for comparisons.
How long is the strand?
The centreline length comes from adding many tiny pieces along the curve:
L = ∫₀ᵀ √((a + bθ)² + b²) dθ
The model evaluates this expression for an ideal continuous curve. It is not the sum of a few complete circles: the radius changes continuously as the angle increases.
From length to an approximate volume
If we also assume a uniform circular cross-section of radius q, the volume of the strand is approximately V ≈ πq²L, provided the strand does not overlap itself. Real ridges, pores, variable thickness, and cooking changes make that assumption imperfect. Volume alone cannot give weight without appropriate density information.
Symmetry, and its limits
A circle repeats exactly under rotations about its centre. A finite spiral generally does not: after a rotation, its radius and endpoints do not match the original curve exactly. Looking round is not the same as having exact rotational symmetry.
No golden ratio, Fibonacci rule, calorie value, or product measurement is implied by the model. A real murukku may not follow this spiral at all.