Strange Attractor Search

If your browser supports Java, you will see above an endless succession
of fractal images produced by the iterated map xnew = a +
bx
+ cx^{2} + dxy + ey +
fy^{2},
ynew
= x, znew =
y, with a through f chosen
randomly over the range 3 to 3. Only those cases that are bounded and
exhibit sensitive dependence on initial conditions (chaos) are exhibited.
The other 99.7% are discarded. Each iterate is plotted at (x, y)
in a hue proportional to
z. Like snowflakes, these strange attractors
come in infinite variety with no two the same. Each one you see is new
and almost certainly has never been seen before.
The technique is described in detail in the book Strange
Attractors: Creating Patterns in Chaos by J.
C. Sprott. The
Java source code is available.
A DOS executable version of the program is available,
along with BASIC source code.
Back to Sprott's Fractal Gallery