# Tornado

Curve · (x, y, z) = f(u, t)

`(3u/tau · cos(10u + t),  4u/tau − 2,  3u/tau · sin(10u + t))`

[Open in the app](https://www.wavelace.com/app#p=44) · [This page](https://www.wavelace.com/presets/tornado)

### What it draws

The second expression, `4u/τ − 2`, is the height. Since `τ = 2π` makes `u/τ` run from `0` to `1` over one turn of `u`, the height climbs at a steady rate from `−2` at the start to `2` at the end. The other two expressions set the same `3u/τ` against a cosine and a sine of the angle `10u + t`, which is a circle of radius `3u/τ`. So the point turns about the vertical axis while its distance from that axis grows evenly from `0` to `3`.

The `10` gives it ten turns in the climb, one coil every `0.4` of height. Every point satisfies `distance = 0.75 · (height + 2)`: the funnel is a cone standing on its point, with a half angle of `arctan(3/4) ≈ 36.9°`.

### Why it spins

The clock enters only as a phase added to the angle, so `t` does not change the shape at all. It rotates the whole cone about its vertical axis, one full turn every `2π ≈ 6.28` seconds at `Speed` 1. That is why the figure reads as a funnel rather than as a static wire. Unlike most curve presets this one is open, not closed: it has a bottom tip on the axis and a top rim of radius `3`.

### Try

- `Top`: from above the coils flatten into a spiral whose radius grows in step with its angle, ten turns of an Archimedean spiral.
- `Front`: the straight sloping sides of the cone, and the coils crossing them.
- Change both `10u` to `20u`: twenty coils in the same funnel, one every `0.2` of height.
- Replace `3u/τ` with `3` in the first and third expressions: the cone becomes a cylinder and the curve is a plain helix.
- Raise `Trail` to 80: the swept copies fill the coils in, and the wire reads as a solid skirt.

### Read more

- [Conical spiral](https://en.wikipedia.org/wiki/Conical_spiral)
- [Helix](https://en.wikipedia.org/wiki/Helix)
- [Archimedean spiral](https://en.wikipedia.org/wiki/Archimedean_spiral)
- [Cone](https://en.wikipedia.org/wiki/Cone)