Fractal Leaf Art

Fractal Leaf Art

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 Capturing the detailed fractals of nature's leaves allows us to develop a stronger understanding of what fractals are all about!

Overview

Many of us won't learn about fractals in detail until we enter college, but fractals are actually quite easy to understand and can be found around us every day! Fractals are a special type of pattern, making them even more desirable to teach to young students as they are discovering patterns in their world around them every day.

This great art activity welcomes creativity, going out for a nature walk, and exploring details to discover how fractals are formed and to create a colorful work of art!

Materials

  • Watercolor paper
  • Watercolors
  • Paintbrush(es)
  • Crayons or pastels
  • Cup of water
  • Any leaf of your choice
  • Optional: poster board

Project Background

Before we dive into our project, we need to ask: What is a fractal?

A fractal is a never-ending pattern within a pattern. It is an object or shape that displays self-similarity: that means that the object is made up of smaller versions of itself, a geometric pattern where every shape represents the whole.   The most popular example of a fractal is a tree:

We can see that a tree starts with a simple shape: the letter Y. Each Y breaks apart into more Y's. We can keep drawing the tree to have more and more branches simply by breaking apart every Y into another Y.

The pattern here is within itself. We usually think of patterns as something that occurs over and over again, like stripes. But fractals are a shape within a shape, not a shape after a shape.

Pattern, but not a fractal:                                             A fractal, which is a special type of pattern:
                                                 

Fractals do not have to be just branches breaking apart into new branches. Any shape or object that is made up of smaller versions of itself or demonstrates the shape breaking apart into smaller versions of that shape is a fractal.

More examples of fractal shapes:

Image from http://mathworld.wolfram.com/

Project Details

STEPS:

0. Now that we know what a fractal is, let's take a nature walk! Visit one of the local parks or waterfalls, or even just take a stroll down the street and back. Pick a couple of your favorite leaves.

1. Select one leaf to start with and look at the veins of the leaf. Start by looking at the very center stem that divides the leaf in half.

 

Now look for the large veins that directly branch off the center. We'll call these primary veins the first level of fractals. These are the base fractals of the leaf that will break apart into more veins. How many of these veins do you see?

 

Now look for the veins that branch off the last veins you looked at. We'll call these the second level of fractals. There's probably already too many to count now! But can you see the difference in the levels of fractals?

 

Can you observe an even smaller level of fractals on the leaf? We'll call these the third level of fractals. How many levels of smaller and smaller branching veins can you see?

 

 

2. Now that we've analyzed the fractals on the leaf, let's see if we can capture it onto paper! Lightly sketch the outline of the leaf onto your watercolor paper using a pencil. If the leaf is already large, consider tracing its outline directly onto the paper. If the leaf is small, consider drawing a larger scale version of it. Take note of how many points the leaf has, what kind of shape it is as a whole, and the curves of its edges between each point.

3. Begin sketching the fractals, still using your pencil. Start by drawing the center stem that divides the leaf. Look again at the large veins that branch directly off of the center. Sketch those onto your paper. Now look again at the next level of veins that branch off. There may be too many of these to capture 1-for-1, but draw what you can to capture the size and look of this third level of fractals!

4. Do you have enough room to draw in another level of tiny fractals? If you dare, go ahead and sketch them in!

5. Grab 2-3 different colored pastels. (Crayons can be substituted if pastels are not available.) Begin by outlining the first level of fractals in one color. Then select another color to outline the next level of smaller fractals. If you were able to draw in a third level of tiny fractals, choose a third color for that final level. You can get creative in color combinations here: you can choose to select colors that are all warm or cool, or maybe choose vivid contrasting colors! You're the artist - get creative!

 

 

6. It's watercolor time! If you are doing this project indoors, be sure to lay down some newspaper first. Select at least two different colors - one for the leaf and one for the background - that will contrast against the fractals. For example, if you chose warm colors for the fractals (red, orange, yellow), consider using cool colors (blues, greens, purples) for the background. Paint your work of art however you like. The pastel outlining of the fractals will allow them to pop out against the watercolor, making for a very vibrant piece!

Once you've completed your watercolor painting, set aside to let dry.

 


7. Optional: Create a backdrop frame. Take a piece of white poster board and cut a square, rectangle, or any shape larger than your watercolor paper. Decorate your poster board any way you like. When your watercolor fractal art is done drying, glue it to the center of your poster board. You now have an even more popping work of art!

Discussion

Our brains better retain information when we engage both our hands and minds in the activity. Now that we've explained how to engage the hand, what are some discussion questions to engage the mind during the activity?

1. How do fractals differ between leaves? That is, what are some differences between the fractals of different types of leaves? What are some similarities?

2. Where else do we see branching fractals in the world around us? What about on our bodies? What about in our bodies? 

3. Where else do we see fractals in nature that are not branches (other shapes that break apart into the same shape)?

4. Look around you and see if you can find a pattern. Is that pattern also a fractal? Why or why not?

5. Can you make up your own fractals?

Supporting Resources

Learn more about fractals!
http://mathworld.wolfram.com/Fractal.html

See a 5-minute, clear video explaining what fractals are:
https://www.youtube.com/watch?v=XwWyTts06tU&feature=youtu.be

Advanced fractal discussion:
http://www.fractal.org/Bewustzijns-Besturings-Model/Fractals-Useful-Beauty.htm

 

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