Spiral in a snail’s shell is the mathematically same as the spiral in the Milky Way galaxy, and it’s also equivalent to the spirals in our DNA. This post has nothing to do with DNA, Snails or the Milky Way!
What’s this?
It’s a category of shapes that are formed by a combination of a spiral and a sphere. Wolfram describes it this way:
Spherical Spiral Curve : The spherical curve taken by a ship which travels from the south pole to the north pole of a sphere while keeping a fixed (but not right) angle with respect to the meridians. The curve has an infinite number of loops since the separation of consecutive revolutions gets smaller and smaller near the poles.
Let’s have a look at the equations which describe a Spherical Spiral Curve :
$x = cos(t)cos(c)$
$y = sin(t)cos(c)$
$z = sin(c)$
_{where}
$ c = tan^{1}(at)$
❝ Why not create a visualization out of it? ❞
— I thought to myself and here it is :
Notice when is changed to zero,
corresponding points form a ring and then they spread out as `a` increases or decreases.
Above visualization is a little different from mathematical reality  time in the visualization goes back and forth between some values so that the behaviour oscillates. Mathematical reality is that it’s a non periodic motion and the path is infinitely long because it’ll keep spiraling into smaller radii as it nears the pole.
Notice how a spiral feels different when it’s stroked compared to when it’s represented with some of its points. There’s a spiral hidden among that distribution of points in 3D space  I couldn’t have guessed. Sampling^{1} really does affect how we think. And we never know how ridiculously sampled information around us is.

Sampling is reduction of information in general. When we discard excess data points to get a simpler picture of something, we’re sampling our data. This saves us memory and processing, but may also result in dangerous inaccuracies. ↩