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 necessary or even possible that the fractal is infinite in size and that when we zoom out , we get selfsimilarity too ?
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 ?