Do you ever wonder what mathematicians study, and why? Most of what they do is complex and inaccessible to laymen, but fractal art might give us a glimpse. While mathematicians study fractals formally, they are used in many branches of science and technology, and we, as laymen, are struck by their beauty. Are you eager to create one? In this activity, you will get to take out some finger paint to make artwork and discover how common fractals are.
This activity is not appropriate for use as a science fair project. Good science fair projects have a stronger focus on controlling variables, taking accurate measurements, and analyzing data. To find a science fair project that is just right for you, browse our library of over 1,200 Science Fair Project Ideas or use the Topic Selection Wizard to get a personalized project recommendation.
Fractals are geometric figures, like triangles and circles. They are hard to define formally, but their features and beauty make them accessible and intriguing.
One feature is self-similarity, which describes how fractals have patterns that recur at different scales. In other words, when you zoom in, you will find a smaller version of a pattern you had seen initially. When you zoom in some more, you will find an even smaller version of that pattern, and so on. This seems to go on infinitely.
The way fractals scale is another feature that sets them apart from traditional geometric figures like lines, squares, and cubes. When you double the length of a line segment, the original line segment will fit twice (or 21) in it, making a line one-dimensional. If you double the length of the sides of a square, the original square will fit four (or 22) times in the new, bigger square, making a square two-dimensional. Do the same on a cube, and the original cube will fit eight (or 23) times into the new figure, making the cube three-dimensional. Apply this operation on a fractal, and the number of times the original fractal fits into the bigger one could be 3 or 5 or any other number that is not a whole power of 2. This is characteristic for fractals. They have a fractional dimension, like 8/5.
A last surprising fact: some fractals can show an infinite perimeter, while their area is finite. This is something you can explore in the artwork you are about to create.
Extra: Look closely at a broccoli crown or Romanesco broccoli. If you cannot find one in the store, look up some pictures on the web. Can you see how the same patterns occur at different sizes?
Extra: Look around you. Can you find fractals in nature? Look at trees, leaves, ferns, and even clouds. Are these fractals too? Why or why not?
Extra: Some fractals consist of a figure containing infinitely many smaller and smaller versions of itself inside. Follow the link listed in the “More to explore” section to learn about the Sierpinski Triangle. Watch the video as it zooms in. Do you see how the pattern infinitely repeats itself at smaller and smaller scale? Can you draw a Sierpinski Triangle? Can you make up a fractal of this type yourself?
Extra: Look on the web for some images of computer-generated fractals and fractals occurring in nature. Do you find them artistic?
Observations and Results
Did you find recurring patterns at different scales? Did you see branching patterns occur? This is what is expected.
The paint likes to stick together. The interactions within the paint and between the paint and the plastic cover give rise to beautiful fractals when you first squeeze the paint between the covers and then release or pull the covers apart. Printing on glossy paper allows you to repeat the process and create patterns that show finer branching.
While the area of your figure is not changing much, its perimeter grows fast when more and more branching is added.
Fractals are common in nature. Trees, leaves, ferns, shells, lightning, and clouds are just some examples. Fractals are not only around us, but also inside us: our lungs and blood vessels show fractal characteristics. Fractal mathematics can help us describe and quantify these structures. Engineers also use fractals to create new products, like cell phone antennas. Fractal art is a form of digital art, where artists use computer-generated images to create intricate objects of beauty.
More to Explore
Sabine De Brabandere, PhD, Science Buddies
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