Looking for equation that matches graph (image inside) I've been trying to come up with a one-variable function that roughly matches this graph:

The closest I've gotten is  $ f(d) = \dfrac{\log(c \cdot (1 - \frac{d}{c}))}{\log c} $, but this approaches $y=0$ at $x=c-1$, and steadily declines from $x=0$, instead of sharply.
Are there any functions or tricks I could look into to develop this further?
Thank you.

Let's try it in polar coordinates (as suggested by John).
We will start with a four petals flower getting the polar expression 
$$\rho=\frac{m-1+\cos(4\theta)}m$$ 
$m$ is a parameter and $m\approx 5$ seems appropriate giving :

In your case the graph will be obtained by 
$$x=C\rho \cos(\theta),\ y=\rho \sin(\theta)$$
To rewrite it with just one parameter you may use $\ u:=\cos(\theta)$ getting :
$$\rho=\frac{m+8(u^4-u^2)}m$$
$$x=C\;\rho\;u,\ y=\rho \sqrt{1-u^2}$$
But $y$ is not a simple function of $x$ and worse the bump at the left is a little too large and the middle part not smooth enough... (but it had to be tried!)
