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I am happy to present a new (I hope new ) fractal - Perpendicular Multibrot. One axis of it - power, other axis is some line (maybe curve) in the complex plane.
For example
In the first image:
x - power axis -3+5
y - real axis -1.5+1.5
In the second image:
x - power axis -3+5
y - imaginary axis-1.5+1.5
I think interesting points of the Mandelbrot set will be interesting here too.