I have been trying to implement the decomposition colouring method as done by Ultra Fractal. The code is trivial:

    double result = atan2(zy, zx);

    if (result < 0.0)
    { result += TWO_PI; }

    return result;

To be exactly the same as the Ultra Fractal implementation the return value should be: result / TWO_PI . But this makes no difference to the problem I am experiencing. My version of the colouring gives sharp lines in the colours along the bands, e.g. on the positive x-axis and many other places. I compared my result to other fractal programs such as Saturn, and they look like my output. Therefore I conclude that Ultra Fractal is doing something else to the angle to avoid these lines? Any insights would be most welcome. Many thanks.

I have attached two images, the first is from Ultra Fractal and the second from my program.

Linkback: https://fractalforums.org/index.php?topic=1557.0

Thanks hobold. I'm not convinced that is the problem, but I will definitely investigate the possibility.

Ahhh, that's why Ultra Fractal divides by TWO_PI - to normalize the result between 0.0 and 1.0 - honestly, sometimes I am so thick :-)

It definitely didn't work before even with dividing by TWO_PI, but I have changed the colour indexing since then. 

All works now! Just had to make sure my colour density value was set correctly.

EDIT: Yes, it works correctly with whole number colour densities of 1 and higher but not with other densities, that's what confused me.