magnification because you will just see more Mandelbrot sets.
Before Mandelbrot
Like most things in mathematics, discoveries are rarely brand new. Looking
into the history Mandelbrot found that mathematicians such as Henri Poincaré
and Arthur Cayley had brief glimmerings of the idea a hundred years before him.
Unfortunately they did not have the computing power to investigate matters
further.
The shapes discovered by the first wave of fractal theorists included crinkly
curves and the ‘monster curves’ that had previously been dismissed as
pathological examples of curves. As they were so pathological they had been
locked up in the mathematician’s cupboard and given little attention. What was
wanted then were the more normal ‘smooth’ curves which could be dealt with by
the differential calculus. With the popularity of fractals, other mathematicians
whose work was resurrected were Gaston Julia and Pierre Fatou who worked on
fractal-like structures in the complex plane in the years following the First World
War. Their curves were not called fractals, of course, and they did not have the
technological equipment to see their shapes.
The generating element of the Koch snowflakeOther famous fractals
The famous Koch curve is named after the Swedish mathematician Niels
Fabian Helge von Koch. The snowflake curve is practically the first fractal curve.
It is generated from the side of the triangle treated as an element, splitting it into
three parts each of length ⅓ and adding a triangle in the middle position.