For the longest time I thought the zeta curve was some kind of sophisticated equation, but it is astonishingly simple. The "magic" of the zeta zeros only happens because of the 1/2 term in the exponent of the equation below. Any change with this fraction, and the zeros do not converge.
You start with a line segment. You then draw another line segment that starts at the end of the previous line segment, and whose length is shorter than the previous segment. The length of any segment is (1/n)^(1/2) where n is the number of the segment. These segments approach a limit (think of Zeno's paradox).
Finally, you bend each segment by an angle alpha. Technically this angle is in imaginary space, but the visual in Cartesian space just looks like a spiral, where each bend adds an angle, like a bull whip, so that the whole curve spirals back around (after creating other, mesmerizing sub-spirals). Amazingly, this curve always intersects zero (per Riemann Hypothesis). As I mentioned in my other comment, it's very useful to see this curve in 3D space.
