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A fractal is a complex pattern made up of self-similar components. Fractal patterns appear throughout nature: from trees, clouds, rivers, and coastlines to your veins, nerves, eyes, bronchial tree, and your brain. Humans experience less stress and better well-being when looking at nature, and this is driven by fractals. Recent research has found that fractals can reduce stress and mental fatigue for the observer by as much as 60 percent. Through exposure to nature's fractal scenery, your visual system has adapted to process fractals with ease, and that's why it is so soothing to look at these shapes.

This program will explore the mathematics of fractal networks and how they are related to dynamical systems theory, a framework for understanding how complex networks change and develop over time. Studying networks emphasizes behavior that emerges from the interactions of multiple components rather than being pre-programmed.  We will study deep theoretical concepts such as self-organization, emergence and chaos at a lay person level, bringing them to life through examples from physics, chemistry, biology, ecology, sociology and more. 

Fun will be emphasized as a way to enhance learning and comprehension, including applications of fractals to art, music, entertainment and more. We will have fun through exploration in computer and laboratory experiments and in kinetic seminar, where we will discuss readings such as James Gleick's book Chaos, while walking in the woods and playing with objects such as hula hoops. Using applications as a springboard, we will build "fun"damental math skills in algebraic thinking such as ratios, exponents, and mathematical modeling. This will help students prepare for scientific study in future programs such as Integrated Natural Sciences and Computer Science Foundations.