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The standard Mandelbrot set has had its complex plane transformed, i.e. c (or the location in the complex plane) has had the following transforms applied:

inverse fold in (3)
add(0.25), no-op
acosh
add(-0.25), no-op
sinh

Note: the inverse fold in value is the diameter of the circle and where the there are two functions separated by a comma the first function is applied to the real part and the second to the imaginary part.