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Fractals are everywhere

From left, sophomore Allie Foley, sophomore Michael Young, Conrad Cortellini '61 and junior Tori Williams in Cortellini's Scecina workshop.

“...see nature as a magnificent book in which God speaks to us and grants us a glimpse of his infinite beauty and goodness.” — Pope Francis, Laudato si’ 

By Bob Golobish, Vice President of Advancement

They are everywhere in nature. Many are hidden. Others are in plain sight. There wasn’t a word to describe them until 1975. That’s when the mathematician Benoit Mandelbrot coined the word “fractal.” 

In a 2010 TED Talk on fractals, Mandelbrot asked the audience to think of a cauliflower because “'s very complicated and it's very simple, both at the same time.” He went on to say, “ … if you cut ... one of the florets of a cauliflower and look at it separately, you think of a whole cauliflower, but smaller. And then you cut again, again, again, ... you still get small cauliflowers. So the experience of humanity has always been that there are some shapes which have this peculiar property, that each part is like the whole, but smaller.” 

A fractal is a never-ending pattern that repeats itself at different scales. This property is called self-similarity. Although fractals are very complex, they are made by repeating a simple process over and over again. The “peculiar property” that Mandelbrot mentioned is found in galaxies, trees, flowers, broccoli, river networks, mountains, clouds, coastlines, lightning bolts, blood vessels in our bodies, bronchial tubes in our lungs, all are examples of naturally occurring fractals. 

Scecina Memorial High School’s artist-in-residence, Conrad Cortellini ‘61, has been captivated by the complexity and simplicity of fractals since he first read an article in Scientific American in 1985 about how fractal images could be created using a computer. 

That article inspired him to create "Total Perspective Vortex," which has been hanging in the Grand Lobby of Clowes Memorial Hall of Butler University since 1992. The 8-foot x 16-foot computer-generated paper relief has two panels, one with a positive spiral vortex and the other with its spatial compliment. A 25th anniversary celebration took place on November 15, 2017. 

Cortellini started his current project several years ago when he used a computer software program to produce a simulated video feedback fractal. He captured one digital image of the constantly changing fractal and then set out to transform each pixels of the digital image into thousands of 1/2-inch x 1/2-inch paper tubes of varying height. Cortellini calls this basic fundamental unit an “element.” 

Building each element takes time. “It is an intentional, serious work of art and it takes great care to assemble each individual element of the fractal,” Cortellini noted. “There is precision cutting, folding and gluing involved in each element,” he added. 

From the elements, Cortellini is building a three-dimensional fractal that when complete will be 32-feet wide x 24-feet high portrait of Chaos. The work has been subdivided into twelve Quadros each comprised of 25,600 elements. The first 8-feet x 8-feet Quadro was built and is on display at DeveloperTown, an incubator for entrepreneurs near Broad Ripple in Indianapolis. A second Quadro is being built at Scecina. A third is planned for Shortridge High School. Regarding the immensity of his "Feedback Fractal Project," Conrad says. “I believe in doing the most that I can do, not the least.” 

A deep thinker, Cortellini has explored the connection between Fractals, Chaos Theory, Complexity, and Dynamics (the new geometry of behavior) and is eager to talk about all of it. "These new developments in science and mathematics are providing a deeper understanding of complex dynamical systems such as the stock market, the weather, and even human culture," he contends. 

Regarding human culture, Cortellini thinks Chaos Theory can help us understand our "tumultuous times" and our "geopolitical situation." He thinks the world is at a "chaos point" or critical juncture and a new order will soon emerge. This new order, whether it is good or bad for humanity, depends on the choices we make regarding our relationships with each other and the environment. 

All of this has been the inspiration for his "Feedback Fractal Project," which Cortellini sees as a "Monument for Our Time." 

Scecina junior Tori Williams has enjoyed creating the small paper tubes for the project. “I like it. It has helped me develop patience and focus and I like the challenge. My technique has improved,” she noted. Scecina sophomore Allie Foley says she “also like the challenge and doing a small thing that is part of a very big project is rewarding. I like being part of an ambitious project. I didn’t think I would ever have the opportunity to do something like this,” she said. When it comes to fractal vegetables like broccoli or cauliflower, Michael Young, a sophomore who works on the project, likes them both. Tori and Allie, paused for a moment, smiled and said they definitely favor broccoli. 

Skilled artisans from all walks of life are needed to work on the fractal. Scecina students, alumni and parents who want to spend some time working together or just slow down are welcome to participate in the project. The slow, careful work allows the artisan’s mind to escape the pressures of contemporary life and reflect on the beauty of God’s creation. If you are interested in learning more about Cortellini’s project or visiting his studio at Scecina, contact him at

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