Elements of Art: Shape and the Phyllotaxis Spiral

Posted by Michelle Chandra on

One of the main design elements I enjoy exploring in my generative art are shapes, whether regular geometric forms such as circles and polygons, or irregular geographic contours.

I love experimenting with different shapes so much, most of my generative "ideas" involve shapes I want to make and experiment with in my programs! 

If you are new to the elements of art (which include shape but also line, texture, form, etc.), you can find more analysis and critique on the different ways artists use shape in their art in this video from Art Prof.

Phyllotaxis Spiral

Much of plant growth is spiral in nature, including the placement of sunflower seeds which is based on rotational turns of 137.5 degrees, the golden angle! This is known as a phyllotaxis spiral and shows up in plants, flowers, and shells.

The phyllotaxis spiral is a lot of fun to experiment with in generative art! Any of my designs with a vaguely sunflower look are probably a modulated phyllotaxis spiral.

Numberphile has a nice rundown of the math behind a phyllotaxis spiral on their YouTube channel.

Below is a design that is a modulated phyllotaxis spiral, but also maps the distribution of color based on a sine wave.

Dan Shiffman of Coding Train has a great video on coding a phyllotaxis spiral on his YouTube channel.

Phyllotaxis Generative Art and Sine Waves

I recently decided to revisit making spirograph designs that are modulated phyllotaxis spirals after polling my Instagram audience for ideas. One shape I enjoy experimenting with in my phyllotaxis art is a sine wave drawn as a circle! 

To create a circular sine wave shape, I adapted example code posted by Ben Crowder, except I use Processing's beginShape function to create my circular sine wave. If you are new to thinking about drawing shapes in terms of circles, polar coordinates and trigonometry, check out Chapter 3 of Dan Shiffman's Nature of Code on Oscillation.

For my latest design, I decided to experiment with drawing circular sine wave shapes at different sizes and frequencies.

As my program runs, it maps the frequency and size of the shape that is drawn to a sine wave! That means, over time, different shapes are drawn in a natural progression of size and form (meaning the shapes gradually get bigger and smaller over and over again, and also the frequency gets bigger and smaller!)

This design is now available in my shop as a limited pen plot print in two colorways, this one has a psychedelic look to it that is pretty different from my past designs. Available in an orange-blue colorway, or a very pretty green-blue!

I split the design into two different color layers by again mapping to a sine wave as the program runs! Each layer is drawn using Faber-Castell Artist Pitt Pens.

Sine waves show up a lot in my generative art, which makes sense as I love creating patterns, and sine waves are a lovely pattern generator! 

All Generative Art, All the Time

But what if you want to learn more?! Check out these additional blog posts:

michelle chandra of dirt alley design

Dirt Alley Design was founded just off a dirt alley in San Francisco in December of 2016 by artist Michelle Chandra. Inspired by the beauty of street grids, Michelle invented maze maps in which she transforms street grids into mazes. In 2019, she began a new project - generative spirograph prints created with code and drawn with a pen plotter. Follow her on Instagram and Twitter @dirtalleydesign where she posts new spirograph designs daily 

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