SchoolArts Room

The Wonderful World of Fractals

By Nancy Walkup, posted on Feb 12, 2019

Do you aspire to implement innovative ways to incorporate S.T.E.A.M. into your K-12 Arts curriculum? Fractals are an engaging way to celebrate the arts, sciences, and mathematics. Furthermore, fractals are nature’s D.N.A. and examples can be seen all around us, from the microscopic patterns on a snowflake to the vast geographies of a coastline.

Hudson Taylor

The wonderful World of Fractals

Connecting math, science, and digital art.

Kevin Fogleston

SchoolArts Magazine, March 2019

As a Graphic Arts teacher at the middle school level for twelve years, I have developed various lessons that utilize cross-curricular concepts so students can gain better insight into the creation process. Fractals have been an exciting way to introduce math and science into my curriculum while captivating students’ interests as they create their digital artworks.

Francesca Matthews

Introducing Fractals
When I first introduce my fractal lesson, students become aware that, for centuries, the brightest minds have struggled to unlock the mysteries hidden within a fractal.  Benoit Mandelbrot was the first scientist to graph a fractal set using IBM computers to calculate complex mathematical equations. Mandelbrot’s exploration with new technology connects with my own passion to utilize the latest technology to create my own artwork and improve my Graphic Arts curriculum. 

In addition to providing my students with a historical context, I emphasize the visual nature of fractals through plenty of engaging examples.  Koch’s snowflake demonstrates the fundamental concepts of fractals both visually and mathematically.  Artist Katsushika Hokusai’s portrayal of nature reinforces repetition and pattern through the use of fractals in many of his woodblock prints.  The splatter of an abstract expressionist painting by Jackson Pollock exhibits self-similarity that represents fractal ideals.  The more students understand the essence of fractals, the more motivated they will become to create mesmerizing fractal artworks.

Katie Heiden

Moving to the Computer
Once students embrace the wonderful world of fractals, they begin designing their fractal mandala artwork on the computer.  Using a variety of fractal generator programs, students create and save high-resolution fractal images that will be utilized in their final mandala designs. I found it beneficial to research online and download fractal generators that were user-friendly and produced a variety of fractal designs.  Furthermore, I required students to save fractal images at a high-resolution to deter their designs from becoming pixelated.  
Once students have designed a plethora of different fractal images, they begin placing and blending their fractal images onto a “pie” piece on the mandala template.  I designed a template in Adobe Photoshop as a tool to aide in students’ fractal mandala designs.  Along with the template, students also follow my step-by-step tutorial and in-class instruction to guide them through the design process.  

Once students complete the pie in Photoshop, they place a background fractal image that compliments the pie shape in the foreground.  It is critical that students also use a background fractal image that creates contrast from the fractal pie.  I encourage students to lighten the pie and bring out the color saturation in Photoshop to make the pie pop out from the background.  Even though I meticulous prepared for this lesson, I developed the best strategies to teach fractal mandalas by learning from my students. 

As students applied their skills, there were steps in the tutorial that they found challenging.  As a result, I tweaked my tutorial to provide more clear and efficient instruction for the difficult tasks. I added complete Photoshop screenshots with the keyboard shortcuts demonstrating how to complete the task so students could have a better visual understanding and work faster. I also observed many students who struggled to line up the pie pieces so the center of the pie cleanly fit together. To resolve this issue, I had these students duplicate the completed pie and shrink down the pie copy to the middle so the center of the pie looked more aligned. This new step was later added to the tutorial as an option that students can apply to their fractal mandalas.  

Jimmy Kania 

Creating artwork with fractals promotes many facets of cross-curriculum learning. With the excitement surrounding S.T.E.A.M. initiatives and the possibility of collaboration with the science and math department, incorporating fractals into your art curriculum can also help you discover a whole new world of learning.  Fractals in art are an engaging way for art, science, and math to coexist in harmony while your students comprehend the fundamentals of fractals and produce artwork that is extremely unique and inspiring.

Logan Voelz

Kevin Fogleston is a graphic arts teacher at Antioch Upper Grade School in Antioch, Illinois.

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