Magnifying to the size of the
universe 
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One of the most beautiful areas of mathematics is a field called complex variables. Much of its detail was worked out in the 1800's. We can create artistic visions with it of incredible beauty. It has many, many practical applications and takes the researcher into other dimensions. For example numbers are two dimensional rather than one dimensional like we are used to in our everyday life. This is something that good 11th graders now understand. I got a call from one a couple of months ago. He had a question about something called the Mandelbrot Set. This is a very simple function in the complex plane, but it can be very beautiful. I explained it to him on his blackboard and then moved to his computer to show him some examples. He said "Ah, I understand!" He then went and got his IPhone and downloaded some beautiful examples. He said: "Now I know what these are!" It took about 15 minutes from start to finish for the explanation and his understanding. We've included a very unusual one in the video above. It shows a self repeating expansion of a very simple complex variable equation called the Mandelbrot Set. This is just one example of millions of these beautiful things. If you run it (takes about 10 minutes), you will see an expansion and a magnification that will equal the size of the known universe. Here is the story of the creator of this little video. The final magnification is e.214. A magnification of e.12 would increase the size of a particle to the same as the earths orbit! e.21 would make a particle look the same size as the milky way and e.42 would be equal to the universe. This animation took me about two days to set up. My computer then rendered day and night nonstop for just over a month to produce the animation The animation was done by 'teamfresh' and we received it from an international group of scientists and mathematicians. teamfresh used extended integer precision in order to generate the gigantic numbers. The animation is about 10 minutes long and it will take you from a particle to the size of the universe after 13.7 billion years.

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