Free Essays on Fractals

In 1979 Mandelbrot produced a computer generated image of what later became known as the "Mandelbrot Set". This set covers a region in the complex C-plane with the property that values of C within this set, or on it's boundary, result in "Connected Julia Sets", and values of C outside the Mandelbrot set produce NC Julia sets that are just clouds of discrete points, or Cantor dust sets. The boundary of this set is very complex. Extending from the perimeter of the large central area are several large and and many small circular bumps, plus numerous thin filaments, which branch out in uneven shapes and contain small islands shaped like miniature versions of the main section. Their results were of mild interest to a small group of pure mathematicions, and were ignored by everyone else. In the 1970s, an applied mathematician, Benoit Mandelbrot, working at the IBM Research Laboratory, did some computer simulations for these sets on the reasonable assumption that, if you wanted to prove something, it might be helpful to know the answer ahead of time. Mandelbrot had been one of Julia's students in 1945, and he was familiar with the papers of both Julia and Fatou. IBM had the best computers available, and a policy of letting research staff members have lots of free computer time to work on anything in which they were interested. Of course, they were also expected to do something useful occasionally. In 1979 Mandelbrot produced a computer generated image of what later became known as the "Mandelbrot Set". This set covers a region in the complex C-plane with the property that values of C within this set, or on it's boundary, result in "Connected Julia Sets", and values of C outside the Mandelbrot set produce NC Julia sets that are just clouds of discrete points, or Cantor dust sets. The boundary of this set is very complex. Extending from the perimeter of the large central area are several large and and many small circular ... Free Essays on Fractals Free Essays on Fractals In 1979 Mandelbrot produced a computer generated image of what later became known as the "Mandelbrot Set". This set covers a region in the complex C-plane with the property that values of C within this set, or on it's boundary, result in "Connected Julia Sets", and values of C outside the Mandelbrot set produce NC Julia sets that are just clouds of discrete points, or Cantor dust sets. The boundary of this set is very complex. Extending from the perimeter of the large central area are several large and and many small circular bumps, plus numerous thin filaments, which branch out in uneven shapes and contain small islands shaped like miniature versions of the main section. Their results were of mild interest to a small group of pure mathematicions, and were ignored by everyone else. In the 1970s, an applied mathematician, Benoit Mandelbrot, working at the IBM Research Laboratory, did some computer simulations for these sets on the reasonable assumption that, if you wanted to prove something, it might be helpful to know the answer ahead of time. Mandelbrot had been one of Julia's students in 1945, and he was familiar with the papers of both Julia and Fatou. IBM had the best computers available, and a policy of letting research staff members have lots of free computer time to work on anything in which they were interested. Of course, they were also expected to do something useful occasionally. In 1979 Mandelbrot produced a computer generated image of what later became known as the "Mandelbrot Set". This set covers a region in the complex C-plane with the property that values of C within this set, or on it's boundary, result in "Connected Julia Sets", and values of C outside the Mandelbrot set produce NC Julia sets that are just clouds of discrete points, or Cantor dust sets. The boundary of this set is very complex. Extending from the perimeter of the large central area are several large and and many small circular ...