Complex Systems
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The Whirlpool/Taffy - The Stingray

Discovered by Jeremy Avnet, Eric Berenson, Brian Martin and Matt Chisholm (though probably described by someone previously).

These pictures come from the function:
z -> (k/z - x/k + z*y/k)n
where k and n are real-valued parameters.

There is quite a bit of weirdness going on here. Notice how there is no c-value in the equation above. For this reason, calling these maps Julia sets would be a stretch. The question of how to take the Mandelbrot-style portrait of the entire parameter space is open as well. For example, one could consider k=c, k=re(c), k=im(c). Or one could consider:
im(c)/z - x/re(c) + z*y/re(c)

How did we come up with this function? The short answer is: Bad communication, and two typos.

All images are 10x10 units, with (0,0) as the center.

0.5M Graph of Exponent vs. Parameter
dynamic Graph of Exponent vs. Parameter (java version)
1.2M 200x200 Animation varying paramater from 0.1 to 4.1.
2.6M 300x300 Animation varying parameter from 0.1 to 4.1.

Last modified: Thu Jun 29 14:14:40 PDT 2000
Pages maintained by Jeremy Avnet; email: jeremy(at)