Here's a setup that satisfies your criteria of sequentially growing arcs stitched together at their ends:
You want a flexible amount of copies of the arcs, so you can't really use the
Switch node since that's a static either this or that node. Instead:
- create an arc,
- make a bunch of copies with
- scale them up sequentially using an
- flip every other arc downwards by selecting them with
Index > Math—Modulo: 2 and scaling them $-1$ on the Y axis.
I also delete the first duplicated instance and replace it with a copy of the original arc so I can use its Sweep Angle option without affecting all the copies.
Short summary of how Accumulate Field works: It takes a Value and continually adds multiples of that value to the chosen elements (domain) according to their index. For example, if you set the value to $3$, and the domain as Instance, first instance (with Index $0$) gets the value of $3$, second one gets $6$, third gets $9$, and so on... That's what the Leading socket gives you, if you use Trailing it starts accumulating with a $0$, so instead of $(3,6,9...)$, you get $(0,3,6...)$. Then what you do with that field (list of numbers) is up to you. Here we're using it to Scale arcs bigger and bigger. (Another way would be to simply multiply Index with the "growing factor", since
Index goes $0,1,2,3...$ it's already a trailing accumulated field with value $1$)
That satisfies the letter of your intent, but not the soul. It roughly looks like one, but this is actually not really a proper spiral. The tangent at the points they meet is not smooth, and it grows very predictably in equal steps, so you wouldn't be able to replicate the example you say you want. To create a mathematically correct growth spiral, you might want to do it the way @Marty-Fouts shows here in this older answer instead.