Koch Snowflake
The Koch snowflake is a
curve of infinite length with a dimension of 1.261859. It is
constructed by taking an equilateral triangle, dividing each side into
three equal parts, erasing the middle part and inserting an
equilateral triangle into the middle of each side. The process is then
repeated as many times as desired. The curve is named after Niels
Fabian Helge von Koch (Sweden, 18701924) who developed the curve
around 1905.
Julia Set
The term "fractal" was coined by Benoit Mandelbrot in 1975. Fractals
are nonregular geometric shapes that have the same degree of
nonregularity at all scales. Fractals are selfsimilar whether you
view them from close up or very far away.
The Mandelbrot Set is a fractal is produced by the
formula z_{z+1}=z_{n}^{2} + c, where z and c
are complex numbers, z_{0}=0, and c is a variable point on the
plane. The formula is iterated until z_{n} ≥2.
The Julia Set, described by Gaston Julia in 1918, is
also a fractal which is based on the same formula with c as the
constant and z as the variable. There is a Julia Set for each point on
the complex plane. The stamp shows a part of the pattern produced when
c=0.2860 + 0.0115i.
