Lesson of the Day: ‘Cauliflower and Chaos, Fractals in Every Floret’

Lesson Overview

Featured Article: “Cauliflower and Chaos, Fractals in Every Floret” by Sabrina Imbler

When two scientists tried to recreate cauliflowers in a lab, they found themselves perplexed and mesmerized by the vegetable’s fractal structure.

In this lesson, you will learn about fractal geometry and some of the ways that it appears in nature. You will closely read the opening of the article to match vocabulary words with their context. Then you will have the opportunity to draw a fractal pattern or photograph 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 about this image?

• What do you wonder?

• Do you see any patterns in this picture?

• What do you think this is a picture of? Why?

The Reveal

This is a picture of a vegetable: the Romanesco cauliflower. This type of cauliflower provides an example of a naturally occurring fractal structure. Margaret Wertheim explains how to recognize fractals in the article “Many Hands Make Fractals Tactile”:

Fractals possess the strange property of “self-similarity.” Zoom in on any part of a fractal, and each small section will have the same richly complicated structure as the whole.

Revisit the image above with this concept in mind. What patterns do you see? Zoom in to the image to see if you can notice the patterns replicated at a smaller scale.

Questions for Writing and Discussion

Instead of starting with the article itself, you will read the first few paragraphs as they appear in our related Vocabulary in Context quiz. This means that one word per paragraph has been replaced with a blank, and you’ll have to choose how to fill it in based on your knowledge of vocabulary and the context of the sentence.

It’s not as hard as it sounds — in fact, paying close attention to the author’s word choice as she introduces key concepts might make reading the rest of the article easier.

Now read the rest of the article, picking up where the quiz left off. This article includes some scientific concepts and other vocabulary you may be unfamiliar with. As you read, you might want to consult as reference this glossary of advanced vocabulary from the piece.

Then, answer the following questions:

1. In your own words, what is a cultivar? Consult the glossary if you are not sure. Of what plant is cauliflower a cultivar?

2. “There is no way you cannot notice it is such a gorgeous vegetable,” Dr. Parcy said, in reference to Romanesco. Do you agree? What do you consider your favorite plant, if you have one? What do you consider 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 did Dr. Godin and Dr. Parcy take to model how cauliflower developed from Brassica oleracea?

5. In your words, describe the process by which a cauliflower grows.

Going 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 triangle shape to explore how fractals replicate the same pattern at different scales, over and over.

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

• Measure the side length of the largest triangle and write it down. Then, measure the side lengths of the next few smaller triangles. What do you notice about these numbers?

If you have extra time, you may even create a three-dimensional version of a Sierpinski triangle.

Option 2: Find and photograph geometry in your own life.

This article is a good example of the fact that geometric concepts do not only exist in the pages of your math textbook — you might find them in nature or on your dinner plate.

Where else can you find geometry in your life? Find an example, photograph it and report back to your class. Write a two-sentence caption for your photo explaining what geometric concept it captures.

In the articles below, New York Times journalists explored how geometry is all around us: in nature, sports formations and even pasta. Choose one article and look through the images to get inspiration for your own.

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