How to Create a Fractal

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Grab a pen and paper and get ready to read this lesson that teaches you how to draw your very own fractal. Learn how you can get some really neat designs this way. Also learn the defining characteristic of fractals.

Fractals

Look at this image.


draw fractal


This shows the stages of building a fractal with just one triangle. You can see how this one triangle is simply repeated within itself. And that is the definition of a fractal. A fractal is an image where you have a never-ending repeating pattern within itself. The fractal you just saw has a special name called the Sierpinski triangle. Look carefully and you'll see how this fractal has the same original triangle being repeated inside of itself. As the pattern is repeated, you get a pretty cool design.

The Steps

If your pen and paper are handy, let's now get started with the steps to draw your very own fractal. These steps are general so you can use them to draw any type of fractal.

1. Draw a large version of a shape or image that you want to be repeated within itself.

2. Choose a rule that you'll repeat over and over.

3. Apply this rule to your image or shape over and over.

4. Keep going until you can't draw the details.

It's a simple process that can yield pretty complex pictures. Let's see how you can use these steps to draw your very own Sierpinski triangle.

Step 1: Draw a larger version of a shape or image that you want to be repeated within itself.

The first step has you drawing a large version of something you want to be repeated. In the case of the Sierpinski triangle, it will be a large black or otherwise fully colored equilateral triangle. Here is your first large black triangle.


draw fractal


Step 2: Choose a rule that you'll repeat over and over.

The next step has you choosing a rule that you'll repeat over and over to draw your fractal. For the Sierpinski triangle, this rule says that you'll draw an upside-down white triangle within any larger colored triangle. So you draw an upside-down white triangle inside this first black triangle.


draw fractal


Step 3: Apply this rule to your image or shape over and over.

After you've decided on your rule, you'll just keep repeating it over and over and over.


draw fractal


The End Result

The last step gives you your end result.

Step 4: Keep going until you can't draw the details.

Keep repeating your rule until you can't anymore. Your end result is usually a very cool image.


draw fractal


Just look at how tiny your triangles are now. If you can keep going, then, by all means, keep going. If you are drawing on a computer program, you can zoom in to keep going. But you will reach a point where you've zoomed in all the way and can't zoom in anymore. At this point, you'll need to stop.

You have successfully drawn a fractal.

Example

Let's try drawing another fractal.

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