I want a (hopefully continuous) function that can describe the following shape. Although the image is not exact, I want the expression to include an increase in crest amplitudes.
For reference, this is an image of a self replicating nano-scale crack in which the delamination and fracture occurs simultaneously to create these amazing shapes. I am trying to backwards engineer an interaction between these two forces to create specific shapes. In order to do that, I need the position function of the crack front. (this crack front position function is what I am asking about)
It looks like a "bent" sine wave. So something like
$$\alpha(t) = (st+b\cos(2t), a\sin(t))$$
The $b$ affects the "bendiness", the $a$ affects the amplitude and $s$ affects the "spaciness."
e.g. $s=1, a=8$ and $b=1$ produces
Link to play around: https://www.desmos.com/calculator/akokhmswfi
Edit: Based on Alexis Olson's suggestion, here is a model where amplitude grows slowly:
https://www.desmos.com/calculator/zgv64n0voe