STRUCTURE AND LIFE IN THE

MANDELBROT- SEAS

LAJOS KECSKÉS

Abstract: The most famous and known fractal is the so called Mandelbrot-set. It can be given by a very simple iterative mathematical formula: Z_n = (Z_n-1)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 “Mandelbrot-sea”. The depth of this water hides curious mathematical miracles: the arrangement of these bays can come into contact with the series  of the Fibonacci-numbers, with the structure of electron-clouds inside of atoms and even with the biological laws of the genetics. Changing  the exponent of the equation arises the multitude of  mandelbrot-seas 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 Mandelbrot-equqtion occurs a new mathematical pattern: extral.