You're interesting and there seems to be quite some effort behind your ideas.

Although saying that you've created a fractal by your drawing still needs to proved. Now looking at one definition of Planck length.

" The Planck length is related to Planck energy by the uncertainty principle.
At this scale, the concepts of size and distance break down, as quantum indeterminacy becomes virtually absolute.
Because the Compton wavelength is roughly equal to the Schwarzschild radius of a black hole at the Planck scale, a photon with sufficient energy to probe this realm would yield no information whatsoever.

Any photon energetic enough to precisely measure a Planck-sized object could actually create a particle of that dimension,
but it would be massive enough to immediately become a black hole (a.k.a Planck particle), thus completely distorting that region of space, and swallowing the photon.
This is the most extreme example possible of the uncertainty principle,
and explains why only a quantum gravity theory reconciling general relativity with quantum mechanics will allow us to understand the dynamics of space-time at this scale. "

What this says to me is that we have a definition about the shortest possible thing discernable in our three dimensions + time.
It does not guarantee that the scale upward must be defined as whole one or whole multiples of a Planck length.

As a thought experiment you can allow your Planck-length to 'start' anywhere in our 3D universe and that implies that there is no locked measurement of distance if you see my drift. Otherwise you would need to believe in an invisible grid created by static planck-lenghts much alike what you have on your screen ordering your icons. That we can't observe anything smaller doesn't necessarily mean that we can't move our Planck object a half Planc-length.

So even though Planck lengths define what we can observe they don't stop us from 'discerning'/imagining smaller distances according to my view :)