Is shapestacking possible in all fractals?

[TheRedshiftRider]

1. It won't work for Julia fractals (and that includes things like the Koch curve and Cantor set).

Shapestacking is possible in julia fractals as well. If the coordinates are detailed enough. You won't see the minibrot but the doubling will be there.

[Pauldelbrot]

Shapestacking is possible in julia fractals as well. If the coordinates are detailed enough. You won't see the minibrot but the doubling will be there.

Umm, technically no, as in you can't start in a Julia fractal and then stack whatever you want to. But you can do it in the corresponding Mandelbrot, then pick a Julia seed from there, and have the same stacked shapes. Just, the malleability will be gone. The doubling of the shapes in the Mandelbrot around the seed will be there, but you couldn't go to, say, one branch tip in the Julia, zoom in, and eventually get two of that branch tip conjoined, or any of that sort of maneuver.

[TheRedshiftRider]

Umm, technically no, as in you can't start in a Julia fractal and then stack whatever you want to. But you can do it in the corresponding Mandelbrot, then pick a Julia seed from there, and have the same stacked shapes. Just, the malleability will be gone. The doubling of the shapes in the Mandelbrot around the seed will be there, but you couldn't go to, say, one branch tip in the Julia, zoom in, and eventually get two of that branch tip conjoined, or any of that sort of maneuver.

Good point. Thanks.

[xenodreambuie]

What I've found with formulas using absolute values is that there are usually large areas too distorted to be good for zooming, and that these are often more useful for finding interesting Julias (especially with convergent coloring included). However, some formulas do have less distorted areas (particularly near any large bulbs) that are good enough for shape stacking, and multiple mini forms are no impediment. Sometimes I can't tell which form a mini will have until I see it.