https://soundcloud.com/st-csound/rose

A polar equation for "Rose" as rendered in Csound using the wterrain opcode. The audio file uses nothing but a simple sine oscillator morphing between curves/shapes, the wterrain opcode and a little reverb.
You can read more about this equation here.

https://mathcurve.com/courbes2d.gb/rosace/rosace.shtml

To demonstrate the various shapes/curves available I plotted the parametric equations here:

https://www.desmos.com/calculator/mlvxpnctan

The slider C at value .2 shows a 5 petal flower. At .25 you'll see 8 petals. Dragging or playing the c slider (curve parameter) will illustrate the numerous shapes possible, it's quite impressive.

To watch these shapes animated:

https://www.desmos.com/calculator/t8sst0l67j

The same values are in effect. If you set slider c to .2 and play slider t (time) you will see the 5 petals animated on the X and Y axis. A value of .5 will repeat but with 8 petals.

Inspired by the fantastic wterrain2 and sterrain opcodes by Christian Bacher.

Hint: while these "shapes" or curves are performed at audio rate, when played in real-time at significantly slower speeds they make very interesting LFOs that can be applied to panning,  3d spatialization, amplitude, filter cutoff or whatever. 

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