# On a variant of rhodonea curves

Rhodonea curves or rose curves are plots of a polar equation of the form
$$r = \cos(k \theta)$$.

If we specialise to equations with

$$k= \frac{n}{d}$$

for n and d integers (>0), then we have plots of the form below. In the table n runs across and d down

Now, just for fun I considered a slight variant of this given by

$$r = \cos( k \theta) – k$$

The plots are as follows

For another variant I considered

$$r = \cos( k \theta) – k^{-1}$$

I am not sure there is anything mathematically deep here, I just like the images and classify this as some basic mathematical art.