Participate in nature’s patterns
Complex patterns in nature form from simple rules, repeated over time and space. A striking example of this is a process that yields beautiful space filling spirals, as in daisies, pine cones, dandelions, sunflowers, and pine apples.
Learn how to code the golden angle spiral model in either Scratch (simple drag and drop commands), NetLogo (very flexible and thorough for studying emergence), or Python (an advanced language used in all industries). We created the model in all three programs.
Here’s our spiral model in NetLogo (the most flexible model) and also in Python. Here’s our simplest spiral models in Scratch. Below are screenshots of the code in Scratch. Here’s a more interesting Scratch spiral model that’s colored to highlight the spirals. And here’s one that uses moving florets to make the spirals. Using this Scratch model you can see how these kind of spirals appear in pine cones.
Below is a coloring sheet you can download and color. This is output from the above models of golden spirals.
Here’s our movie that applies this model of golden angle spirals to a craft with pinecones based on our computer model of spirals in NetLogo and a similar spiraling model in Python. We see such golden spirals in sunflowers, daises, dandelions, pine cones, pineapples and more.
There is another way to make golden angle spirals which we show here. This version of the model helps show how the golden angle, approximately 137.5 degrees, fills space.
This is also true of daisies and dandelions, the number of spirals are Fibonacci numbers.
Spread out the wire ends at the bottom to make a base. You can place the wire stems in a small flower pot, or cover with paper. This is just a fun craft for adults to complete with young children. Yet it visually emphasizes that both the leaves and spiral florets on the flower head have patterns that optimize space. The spirals on the flower head tightly packs the florets, which later turn into seeds. The folds on the leaf allow the leaf to tightly fold.
All the above is the theme of one of our popular boxes that comes with your subscription to Beautiful Discovery. The box includes our golden ratio spirals science booklets, spirals coloring sheets, real pine cones, computer models of the spiral formation, crafts and much more.