Lesson of the day: “Cauliflower and chaos, fractals in every flower”
Lesson overview
Featured Article: “Cauliflower and chaos, fractals in every flower»By Sabrina Imbler
When two scientists attempted to recreate cauliflower in a lab, they found themselves puzzled and fascinated by the vegetable’s fractal structure.
In this lesson, you will learn about fractal geometry and some of the ways it appears in nature. You will read the opening of the article carefully to match the vocabulary words with their context. Then you will have the option to draw a fractal pattern or photograph some geometry in your own life.
Warm up
Look at the image at the top of this article. Before going any further, answer these questions:

What do you notice in this picture?

What do you wonder?

Do you see any patterns in this image?

What do you think it’s a picture of? Why?
The revelation
Here is a photo of a vegetable: Romanesco cauliflower. This type of cauliflower provides an example of a natural fractal structure. Margaret Wertheim explains how to recognize fractals in the article “Many Hands Make Fractals Tactile”:
Fractals have the strange property of “selfsimilarity”. Zoom into any part of a fractal, and each small section will have the same richly complicated structure as the whole.
Review the image above with this concept in mind. What models do you see? Zoom in on the image to see if you can notice the patterns reproduced on a smaller scale.
Questions for writing and discussion
Instead of starting with the article itself, you’ll read the first few paragraphs as they appear in our Vocabulary quiz in related context. This means that one word per paragraph has been replaced by a blank, and you will have to choose how to fill it according to your knowledge of the vocabulary and the context of the sentence.
It’s not as difficult as it sounds – in fact, paying close attention to the author’s word choice when introducing key concepts might make the rest of the article easier to read.
Now read the rest of the article, picking up where the quiz left off. This article includes science concepts and other vocabularies you may not be familiar with. As you read on, you may want to refer to this advanced vocabulary glossary from the article as a reference.
Then answer the following questions:
1. In your own words, what is a cultivar? Consult the glossary if you are unsure. What plant is cauliflower a cultivar of?
2. “There’s no way you can’t notice that it’s such a gorgeous vegetable,” Dr Parcy said, referring to Romanesco. Do you agree? What is your favorite plant, if you have one? What do you think is the most beautiful plant?
3. Look through the pictures in the article. How does the appearance of cauliflower differ from that of kale, Brussels sprouts, and broccoli, which are versions of the same plant?
4. What steps have Dr Godin and Dr Parcy taken to model the development of cauliflower from Brassica oleracea?
5. In your own words, describe the process by which a cauliflower grows.
Go further
Option 1: Draw a fractal triangle.
One of the best ways to understand fractal geometry is to create it yourself. By drawing a Sierpinski triangle, you will use a triangular shape to explore how fractals reproduce the same pattern at different scales over and over again.
The video below shows how to draw this fractal triangle. As you watch, draw your own on a blank sheet of paper or using this template.

How many triangles in total were you able to draw? How many triangles did you draw in the largest size? How many are the next bigger size, and so on? What do you notice about these numbers?

Measure the length of the side of the larger triangle and write it down. Then measure the length of the sides of the next smaller triangles. What do you notice about these numbers?
If you have more time, you can even create a threedimensional version of a Sierpinski triangle.
Option 2: Find and photograph geometry in your own life.
This article is a good example of how geometric concepts don’t just exist in the pages of your math textbook – you can find them in nature or on your plate.
Where else can you find geometry in your life? Find an example, photograph it, and report back to your class. Write a twosentence caption for your photo explaining what geometric concept it captures.
In the articles below, reporters from The New York Times have explored how geometry is all around us: in nature, athletic training, and even pasta. Pick an item and browse the images for inspiration.
About today’s lesson
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