2.29 Henon Attractors
(type=henon)
Michel Henon was an astronomer at Nice observatory in southern France.
He came to the subject of fractals via investigations of the orbits of
astronomical objects. The strange attractor most often linked with
Henon's name comes not from a differential equation, but from the world
of discrete mathematics - difference equations. The Henon map is an
example of a very simple dynamic system that exhibits strange behavior.
The orbit traces out a characteristic banana shape, but on close
inspection, the shape is made up of thicker and thinner parts. Upon
magnification, the thicker bands resolve to still other thick and thin
components. And so it goes forever! The equations that generate this
strange pattern perform the mathematical equivalent of repeated
stretching and folding, over and over again.
xnew = 1 + y - a*x*x
ynew = b*x
The default parameters are a=1.4 and b=.3.