What happens when I choose a different starting value x0?

[cbuchner1]

Hi,

I just tried plotting a Buddhabrot type fractal and instead of the usual x0=(0,0) for my iteration
start value I tried other constant numbers, such as e.g. (0.5, 0). This tuple notation is supposed
to represent a complex number by the way.

The visual results were certainly interesting - but what does a different start value x0 actually
mean? When it is no longer the Mandelbrot set that I am getting - then what is it

I am contemplating to choose two values x0 = (-a,0) and x0 = (+a,0) to generate two
slightly distinct perspectives for a stereoscopic view. Or alternatively x0 = (+a*cos(alpha), +a*(sin(alpha))
for the left eye and x0 = (-a*cos(alpha), -a*(sin(alpha)) for the right eye where alpha is another parameter.

[cKleinhuis]

it is called pertubation, you do not use the same starting value ( like (0,0) -> a complex number, one reason is that it consists of 2 components)
if you see it in a realtime program, you can imagine how the starting value affects the resulting mandelbrot image
but nevertheless, you produce nice variations of the iteration loop, which is visualized by buddhabrots

it is like the julia seed applied to the mandelbrot

i do not really believe that it produces usable stereoscopic results, but nevertheless, it is worth a try if each eye views a different pertubation of the set ...
but it happens to be that the mandelbrot is always moving in the same direction if real axis pertubation values are positive or negative