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).

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-A01-xx in this gallery are generated with 2 functions (fn1(), fn2()) and 3 imaginary parameters (p1, p2 and p3).
These equations cover many other groups of equations, including groups of equations provided by FRACTINT.
Many various images can be generated with them.

The equations used here are very simple.

z = fn1(pixel) ^ real(p1) :
z = fn2(z) ^ p2 + p3,
|z| <= imag(p1)

For the fractal here :
fn1() = cos(), fn2() = tan()
real(p1) = 2, imag(p1) = 5, real(p2) = 3, imag(p2) = 0, real(p3) = -2, imag(p3) = 0.2

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.

Zoom on the center of the above fractal, with another palette of colors.



Below is drawn a zoom of an area of the initial fractal (on the left of the red center) :



The main fractal shown above belongs to an alignment along the x axis of the same image.
The length of the partial image shown below is infinite (along the x axis).