STRUCTURE AND LIFE IN THE MANDELBROT SEAS


Abstract: The most famous and known fractal is the so called Mandelbrotset. It can be given by a very simple iterative mathematical formula: Z_{n} = (Z_{n1})^{2}C. The points of this fractal form a curiously limited shape on the plane of the complex numbers. We can imagine the largest spot as a „sea”, and the smaller ones as “bays” of this “Mandelbrotsea”. The depth of this water hides curious mathematical miracles: the arrangement of these bays can come into contact with the series of the Fibonaccinumbers, with the structure of electronclouds inside of atoms and even with the biological laws of the genetics. Changing the exponent of the equation arises the multitude of mandelbrotseas containing more or less, or  maybe it is unimaginable  “negative” symmetry axis’s. Inverting (mirroring?) the role of the variable and the constant of the Mandelbrotequqtion occurs a new mathematical pattern: extral.
