I got checking working for the , based on Xavier Buff's method for the Mandelbrot set presented by Arnaud Cheritat:

Replace `der` by the Jacobian $L$ w.r.t. $(x_1, y_1)$. Replace `squared_modulus(der)` with $|\det{L}|$. Arbitrarily use the pixel spacing for `eps`.

Should be straightforward to generalize the idea for other formulas.

The red zone of unknown is troubling - I wonder what is really going on in there.

Some progress: (a,b)=(-0.75,-0.25) gives a non-repeating but apparently bounded collection of iterates.

Need to improve my gnuplot skills to colour the points in a comprehensible gradient from first point to last

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(a,b)=(0.25,-0.75) results in a dense pattern

trouble is to show that it remains bounded...

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