Rose, Rhodonea, Curves, aRtVerse, MindFrameShift, geometry, mathematics, line plots, point plots, polygon plots, data art, code art, algorithmic art, generative art, math art, data science, R programming, teepublic

Algorithmic Art: Flowers, Roses and Rhodonea Curves

Rose, Rhodonea, Curves, aRtVerse, MindFrameShift, geometry, mathematics, line plots, point plots, polygon plots, data art, code art, algorithmic art, generative art, math art, data science, R programming, teepublic
In mathematics, a rose or rhodonea curve is a sinusoid plotted in polar coordinates. Available on apparel and other print on demand products

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

Mathematical “rose” or “rhodonea” curves,
based on the polar-coordinates equation r=cos(θ*n/d).
In this chart, the values of parameter n varies from 1 to 7,
while d varies from 1 to 9.
Wikipedia

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

Point Plots

Rose, Rhodonea, Curves, aRtVerse, MindFrameShift, geometry, mathematics, line plots, point plots, data art, code art, algorithmic art, generative art, math art, data science, R programming,

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

Rose, Rhodonea, Curves, aRtVerse, MindFrameShift, geometry, mathematics, polygon plots, data art, code art, algorithmic art, generative art, math art, data science, R programming,

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!

Rose, Rhodonea, Curves, aRtVerse, MindFrameShift, geometry, mathematics, polygon plots, data art, code art, algorithmic art, generative art, math art, data science, R programming,

Add Some Colour

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

  • Rose, Rhodonea, Curves, aRtVerse, MindFrameShift, geometry, mathematics, polygon plots, data art, code art, algorithmic art, generative art, math art, data science, R programming,
  • Rose, Rhodonea, Curves, aRtVerse, MindFrameShift, geometry, mathematics, polygon plots, data art, code art, algorithmic art, generative art, math art, data science, R programming, phone case
  • Rose, Rhodonea, Curves, aRtVerse, MindFrameShift, geometry, mathematics, polygon plots, data art, code art, algorithmic art, generative art, math art, data science, R programming, laptop case
  • Rose, Rhodonea, Curves, aRtVerse, MindFrameShift, geometry, mathematics, polygon plots, data art, code art, algorithmic art, generative art, math art, data science, R programming, mug

Featured Products

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


See More At My aRtVerse Store!

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Phylotaxis, Green, Cacti, Data Art, Code Art, Math Art, aRtVerse, Teepublic, https://www.teepublic.com/user/artverse, Purple, White Geometry, Symmetry, Spiral

Phyllotaxis: Maths creates Beauty & Symmetry in Nature + Free Collages & Mood Boards

Phylotaxis, Green, Cacti, Data Art, Code Art, Math Art, aRtVerse, Teepublic, https://www.teepublic.com/user/artverse, Purple, White Geometry, Symmetry, Spiral
Phyllotaxis inspired designs available on various apparel and products

Last year I started experimenting with mathematical formulas and data algorithms to generate art, specifically using code scripts created in R.

The first time I stumbled upon math art in R was when I saw the phyllotaxis patterns project on DataCamp created by the Mathematician A. Chinchón last year sometime. He maintains an extensive blog Fronkonstin where he regularly publishes new math art projects. He provides all the scripts he uses and encourages his readers to create their own art using these scripts.

I have started to mess around with several of these math art concepts and mashed-up many ideas from around the internet. I am not a mathematician, but I can use R and entertain myself with these scripts to create all sorts of interesting restults. Yes, I am that kind of nerd… LOL!

I have slowly progressed to writing R “art” code completely by myself as well! Those will be featured on the blog in future posts.

Phyllotaxis in Cacti

In botany, phyllotaxis or phyllotaxy is the arrangement of leaves on a plant stem (from Ancient Greek phýllon “leaf” and táxis “arrangement”). Phyllotactic spirals form a distinctive class of patterns in nature.

Some early scientists—notably, Leonardo da Vinci—made observations of the spiral arrangements of plants. In 1754, Charles Bonnet observed that the spiral phyllotaxis of plants were frequently expressed in both clockwise and counter-clockwise golden ratio series. Mathematical observations of phyllotaxis followed with Karl Friedrich Schimper and his friend Alexander Braun’s 1830 and 1830 work, respectively; Auguste Bravais and his brother Louis connected phyllotaxis ratios to the Fibonacci sequence in 1837.

Wikipedia

Phyllotaxis Collages

I originally created these collages from free photos on Pixabay to sell at my design eShop on Zazzle, but I have since closed my store there as I felt that they were ripping-off our designer community – so I left and started anew on Teepublic. These collages do not vibe with aRtVerse’s reincarnation and thus I made them available here as free design resources!

You can find the Pinterest Collage Board Here! Merry Christmas!

Phyllotaxis, Cacti, Green, Geometry, Symmetry, Spiral
Phyllotaxis, Cacti, Purple, Geometry, Symmetry, Spiral
Phyllotaxis, Cacti, White, Geometry, Symmetry, Spiral

Phyllotaxis Mood Boards

I have also created a mood board for each of the cacti collages – several mood board design resources will be made freely available from Mind Frame Shift for your design inspiration!

You can find the Pinterest Mood Boards Here!

Phyllotaxis, Green, Cacti, Mood Board, Colour Palette, Geometry, Symmetry, Spiral
Phyllotaxis, Purple, Cacti, Mood Board, Colour Palette, Geometry, Symmetry, Spiral
Phyllotaxis, White, Cacti, Mood Board, Colour Palette, Geometry, Symmetry, Spiral

Phyllotaxis Inspired Data Art

Here is a close-up look at the spirals I created using R code and taking inspiration from the colleges! Each of these spirals have up to 1000 individual points!

Phylotaxis, Green, Cacti, Data Art, Code Art, Math Art, aRtVerse, Teepublic, https://www.teepublic.com/user/artverse , Geometry, Symmetry, Spiral
Phyllotaxis inspired designs available on various apparel and products @
https://www.teepublic.com/user/artverse/albums/48097-geometric-shapes-and-spirals
Phylotaxis, Purple, Cacti, Data Art, Code Art, Math Art, aRtVerse, Teepublic, https://www.teepublic.com/user/artverse , Geometry, Symmetry, Spiral
Phyllotaxis inspired designs available on various apparel and products @ https://www.teepublic.com/user/artverse/albums/48097-geometric-shapes-and-spirals
Phylotaxis, White, Cacti, Data Art, Code Art, Math Art, aRtVerse, Teepublic, https://www.teepublic.com/user/artverse , Geometry, Symmetry, Spiral
Phyllotaxis inspired designs available on various apparel and products @
https://www.teepublic.com/user/artverse/albums/48097-geometric-shapes-and-spirals

aRtVerse – An Universe where R, Art & Maths Collides

Finally the whole collection of phyllotactic spirals with single or multiple arms inspired by the different ways in which leaves can arrange on plant stems. These designs are available on various apparel and products from my aRtVerse Teepublic eShop! The spirals were generated with individual points using R code in the Inferno/Volcano (top right), Plasma/Sunset (bottom left) and Viridis/Peacock (bottom right) colour palettes.

You will also notice one of those multi-arm spirals in my aRtVerse and Mind Frame Shift logos as well!

Phylotaxis, Green, Cacti, Data Art, Code Art, Math Art, aRtVerse, Teepublic, https://www.teepublic.com/user/artverse, Purple, White Geometry, Symmetry, Spiral
Phyllotaxis inspired designs available on various apparel and products @ https://www.teepublic.com/user/artverse/albums/48097-geometric-shapes-and-spirals

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


See More At My aRtVerse Store!

aRtVerse, TeePublic, Tanzelle Oberholster, Mind Frame Shift

aRtVerse @ Teepublic
ART SCIENCE NATURE


Affiliate Marketers Welcome! TeePublic Affiliate Program

Want to start up your own store? Sign up here as a Teepublic Designer!