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

4 functions can be used and 3 parameters (imaginary numbers).
The maximum number of lignes of code is 2,000.

A large number of functions are available :
sin(), cos(), tan(), cotan(), sinh(), cosh(), tanh(), cotanh(),
asin(), asinh(), acos(), acosh(), atan(), atanh(), exp(), log(),
sqr(), sqrt(), recip(), flip(), ident(), conj(), cabs(), floor(),
ceil(), trunc(), real(), imag(), srand(), abs(), etc.

All the fractals named JMC-C09-xxx in this gallery are generated with 4 functions (fn1(), fn2(), fn3() and fn4())
and 3 imaginary parameters (p1, p2 and p3).
This equations cover many other groups of equations, including groups of equations provided by FRACTINT.

The equations used here are :

z = pixel^real(p1), c = real(p1) * fn1(pixel):
z = real(92) * fn2(z),
z = (imag(p2) * fn3(z) + real(p3) * fn4(z))^imag(93) + c,
|z| <= imag(p1) (bailout test)

For the fractal here :
fn1() = tanh(), fn2() = ident(), fn3() = ident(), fn4() = zero().
real(p1) = 1, imag(p1) = 128, real(p2) = 1, imag(p2) = 1, real(p3) = 0, imag(p3) = 4

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 can be observed, and often no fractal is drawn.
3) Here fn4() = zero() which means zero(x + i * y) = 0.