Fractal type formula.
In this case, the user defines all the equations and the parameters
for the calculations of the fractal (including the palette of colors).

All the fractals named C01-xx in this gallery are generated with 4 functions (fn1(), fn2(), fn3() and fn4())
and 3 imaginary parameters (p1, p2 and p3).

The equations used here are :

z = fn1(pixel) ^ real(p1):
z = fn2(fn3(1/fn4(z))^p2) + p3),
z = (z / (fn3(z) ^ real(p3) + fn4(z) ^ imag(p3))) ^ imag(p2),
|z| <= imag(p1) (bailout test)
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For the fractal here :
fn1() = sqr(), fn2 = ident(), fn3 = ident(), fn4 = acosh().
real(p1) = -4, imag(p1) = 64, real(p2) = -2, imag(p2) = 0, real(p3) = 2, imag(p3) = 0

Notes.
1) Many other parameters are used, but they are too complex to be explained here.
2) If a function is changed or if a parameter is modified (including a very small change),
a drastic change of the fractal may be observed, and often no fractal is drawn.

If real(p1) = -2 instead of -4, the shape of the fractal looks like this :



With the same parameters but with another palette of colors, the fractal looks like this :



If real(p1)= -3 instead of -2, and with another palette of colors, the fractal looks like this :