Dürer Spiral Emission

Overview

This spiral arrangement emerges from the angular formula offset = 2πi / (n × twist), which distributes each curve evenly along the circular domain while layering them with rotational drift. The variable i represents the current spiral’s index out of n total, and twist modifies how tightly the spirals rotate around the center. As the index increases, each curve receives a unique angular offset, creating a nested radial rhythm. The result is a geometric phasing effect where no two spirals align completely, yet all follow a shared rotational order.

Each curve expands outward using the polar equation r = a + bθ, where a is the initial radius and b controls how fast the spiral opens as θ increases. This produces an Archimedean growth pattern, ensuring that the spacing between spiral arms remains consistent. The use of r × cos(±θ + offset) and r × sin(±θ + offset) then converts this growth into Cartesian coordinates. The optional reversal flips the spiral direction, producing mirror-symmetric forms that wind in opposite orientations while still obeying the same radial logic.

The visual texture across each spiral is modulated by the expression sin(2θ + offset + 1)/2, which oscillates smoothly between zero and one. This mapping generates periodic intensity variations along the curves, aligned to their angular position. To deepen the presence of each line, I looped over a range of alpha values using linear spacing from 0.0 to 1.0, layering the same geometry multiple times with subtle transparency shifts. These overlapping emissions create soft halos and reinforce the structure’s depth without relying on randomness, only on repetition and trigonometric rhythm.