This Week's Fractal 21 (z^2-ixy+c)

Hello, this is 108Hassium.

This week, I am presenting fractal figures related to $${z^2-ixy+c}$$ (where $${x}$$ and $${y}$$ are the real and imaginary parts of $${z}$$).

z^2-ixy+c

I previously covered a very similar function, $${z^2+ixy+c}$$, but the shape of the Mandelbrot set seems to be quite different.

※☟Article on $${z^2+ixy+c}$$

Just like with $${z^2+ixy+c}$$, there are Julia sets where the convergence regions are connected, but I feel that this one has more bold and interesting twists in its regions.

These are Julia sets that include white regions (regions that converge to a cycle different from $${z_0=0}$$), a type also seen in perturbed Julia sets and $${z^2+ixy+c}$$.

These are Julia sets with a way of incorporating white regions that I haven't seen very often.

This is a Julia set that has a third convergence region (blue) in addition to the white region.

The usual one.

This is an infinite-period Julia set with a ring-shaped orbit.

This is a strange attractor.

Although the range of c where strange attractors appear is wider than for z^2+ixy+c, the shapes of the attractors were all similar elliptical ones to those of z^2+ixy+c.