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 4 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 numbers (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 = (fn1(1/fn2(pixel)))^real(p1);
z = fn3(fn4(z^p2)) + p3;
|z| =< imag(p1)
For the fractal here :
fn1() = cos(), fn2 = ident(), fn3 = tan(), fn4 = tan()
real(p1) = 5, imag(p1) = 2, real(p2) = 1.5, imag(p2) = 3, real(p3) = 5, imag(p3) = 1
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,
like real(p1)=1 replaced by real(p1)=1.1, a drastic change of the fractal can be observed,
and often no fractal is drawn.
Below, 4 similar images but with other palettes of colors (with rotation of the palette for some of them).
Image C09-010A (2019/02/25).
Image C09-010B (2019/02/25).
Image C09-011C (2019/02/25).
Image C09-010D (2019/02/25).
Below, 6 kaleidoscopic images are displayed (these images are not fractals).
The original fractal used to generate these kaleidoscopic images is C09-010A.
Kaleidoscopic image C09-C10A-K1 (2020/04/30).
Kaleidoscopic image C09-C10A-K2 (2020/04/30).
Kaleidoscopic image C09-C10A-K3 (2020/04/30).
Kaleidoscopic image C09-C10A-K4 = image C09-C10A-K3 but with another palette of colors (2020/04/30).
Kaleidoscopic image C09-C10A-K5 (2020/04/30).
Kaleidoscopic image C09-C10A-K6 (2020/04/30).
