Blog post: ajb: On a variant of rhodonea curves

Rhodonea curves or rose curves are plots of a polar equation of the form

$latex r = cos(k theta)$.

If we specialise to equations with

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

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

$latex r = cos( k theta) - k$

The plots are as follows

For another variant I considered

$latex r = cos( k theta) - k^{-1}$

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

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