It is well known that if we zoom in on the Mandelbrot set we get selfsimilarity. So I wonder if $g$ is a fractal (in the complex plane) generated by a nonperiodic nonpolynomial entire function $f$
Is it possible that the fractal is infinite in size and that when we zoom out , we get selfsimilarity too ? Lets call such a fractal a " zoom out fractal ".
As example Mandelbrot : $f(z)=z^2+1$, g$(z) [= f(f(...))]$ is the fractal. The fractal has finite size (area or length ) since it diverges for $Re(z)>2$. $f(z)$ is a nonperiodic nonpolynomial entire function. But when we zoom out we get no selfsimilarity. ( divergence is not considered valid as selfsimilar ) So Mandelbrot is NOT a zoom out fractal.
Does the existance of zoom out fractals require that the fractal is also a zoom in fractal ?
What is the formal way or term to express ' zoom out selfsimilarity ' or ' zoom out fractal ' , if any ?