My idea is to iterate a function that is z_(n+1)=f(n,z_n), instead of z_(n+1)=f(z_n).
I tried this with a perturbation of the classic formula z-->z^2+c, btaining very nice effects with tan(x).
An example (code in c):

///////////////////
int z;
double tm;
double k1,s,zz;s=rrrr+iiii;

for (z=0;z (minor) maxit;z++)
{
zz=(double)(z);
k1=tan(5zzzzsqrt(s))/(2.0zzzzzz+250000)+1;
tm=rr;
rr=rrrr-iiii+rk1;
ii=2tmii+ik1;
s=rrrr+iiii;
if (s>10000000) break;
}

return z;
////////////////////////

this is the classica mand formula perturbed with the k1 value
some thing about the argument of tan(x)
the zz^2 is something that make the perturbation more frequent when iteration grows, making the perturbation 'constant' while zooming .The zz^3 in the following division is to make the effect of reducing the power of perturbation. You can play changing this 2 exponents, or other parameters.

My last 5 fractals had been with this formula (with some minor variations).
I'm not able to play with UF, or with textur, multilayer, ecc, i only like to play with programmming and mathematic, but i will be very happy if this can be used by UF master to do new images.....

Thanks
HG

Message edited on: 02/12/2006 14:15