## Algorithmic Art: Flowers, Roses and Rhodonea Curves

Algorithmic or algorithm art includes designs generated by an algorithm. Algorithmic artists are sometimes called algorists.

I wrote the R script to generate the featured data art all by myself using the concepts of Rose Curves and in the process was able to have an in-depth look into what really happens during the construction of code-generated flowers.

You can read my introductory post on Math Art with Phyllotaxis, followed by Asteroid Impact, Mandala Dragonflies and Data Dreamcatchers!

## Rose Curves

In mathematics, a rose or rhodonea curve is a sinusoid plotted in polar coordinates.

These curves can all be expressed by a polar equation of the form,

r = cos(kΘ)

Wikipedia

In short, rose curves are interlocking loops connected at a central point, much like one would draw a simple flower with the free hand.

They are created with two parameters when generated by computers:

- n = number of points
- d = number of loops

During construction, the n and d parameter works together to generate the number of petals (as a multiple of k):

- k = n/d
- when k is even then the number of petals equals k (or k*1)
- when k is odd then the number of petals equals k * 2

This makes more sense when you follow the graph below

- n = 1 and d = 1 then k =1 and you get a circle
- n = 2 and d = 1 then k = 2 and you get a four leaf clover (2*2 = 4 petals)
- n = 1 and d = 2 then k = 0.5 and you get half a petal, connected by interlocking loops … you can read more about the exact mathematics on Wikipedia.

The top graph is generated with lines, I generated similar plots using points and polygons.

### Point Plots

It seems that the algorithm merely repeats itself at various places, especially when the ratio between n and d is 1:1 such as along the diagonal line from the top left to right of the image.

However, the polygon plots reveal that this is not the case!

### Polygon Plots

Here you would notice that the plots are generated in repeating loops and that the width/thickness of these loops increases as we move diagonally down the graph.

This makes for far more interesting shapes, especially with the custom colouring that I coded into the loops!

### Add Some Colour

Finally we end up with coloured polygon rose curves as well as some striking product designs!

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**CC-BY-NC 3.0 – Images are free to use for personal and non-commercial projects given attribution to Dr Tanzelle Oberholster**

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