jjwynne

I have taught an appreciation of fractals to elementary school youngsters, including my 7-year-old grandchildren, by having them construct a fractal structure, a Sierpinski tetrahedral pyramid, our of toothpicks and mini-marshmallows. They first construct tetrahedra and then connect them together in stages. The kids get the concept of self-similarity, and the have a great time building a bigger and bigger structure until it collapses under its own weight. See https://www.google.com/search?q=Sierpinski+tetrahedral+pyramid+toothpicks+marshmallows&rlz=1T4GGLL_enUS378US378&tbm=isch&tbo=u&source=univ&sa=X&ei=DaygUr__FIaysATl8oHQAg&ved=0CCsQsAQ&biw=1024&bih=506

Benoit once told me that the best tasting bagels are those with a fractal distribution of holes. If the bagels are cooked at the right temperature, the carbon dioxide generated by the yeast forms bubbles with a fractal distribution. So before you buy a bunch of bagels, cut one open, look at the different hole sizes, and they range from very small to very large, they were cooked properly.

Of course, you can always taste one bagel before buying a bunch from the same batch. But that's not the "fractal way" to judge your food.

Pure mathematics has always been a source of wonder to me. Learning from Benoit that the mathematics of nature is not Euclidian, and seeing that he had a new way of looking at the non-Euclidian geometry of nature, was a source of inspiration to me. But I'm an experimental physicist, not a mathematician. So I'm more a spectator, rather than a practicianer of pure mathematics.

My advice is to continue your study of pure mathematics, but make sure you keep up with computer science. You may decide to use your math skills to create the algorithms that make Google obsolete.

Math is the language of science. We physicists always need new ideas in mathematics to draw together disparate data into a new framework.

Benoit was a very versatile and enthusiastic thinker and expositor. He wanted everyone to know about and appreciate fractals. So he was thrilled when fractals went viral in the 90s. During that time, my daughter was a college student. She interviewed Benoit for a research project for one of her math courses, wrote a nice essay, and posted Mandelbrot Set posters, signed by Benoit, in her dorm rooms. Needless to say, this made him very happy.

One application that was thought to be very important was to design fractal-based antennas for cell phones and other mobile devices. The idea was that a fractal antenna could pick up a larger range of frequency bands on which signals were transmitted. But the downside was that there was lots of noise in this broad range of frequencies, and the fractal antenna picked up this undesirable noise, obscuring the desired signal in the narrower frequency band where it was being transmitted.

So fractal antennas were abandoned. Not everything works as planned. But you have to keep experimenting, and sometimes you find "gold."