How small can the repetitive fractal features of nature get? (Strange Universe Series)

By now, most of us are familiar with fractal images, a fascinating visual representation of a rather simple mathematical formula developed by Polish Mathematician Benoît Mandelbrot. What many of us may not know is that Mandelbrot first wondered How long is the coast of Great Britain? back in the 1960s. One could easily measure the distance from Brighton Beach in the South to Newcastle on Tyne in the North as the crow flies. But how far is it if you have to walk, and can’t step into water? How far if you aren’t a human capable of jumping any stream smaller than 6 feet across, but instead an ant. What if you are a single-celled organism and must get there on dry land? As we look at a section of natural coast land, we find as we zoom in an ever smaller repeating set of rather similar but incredibly exquisite details. In his search for a mathematical approach to answering his original question about the length of the British Coast, Mandelbrot came to his discovery of the Mandelbrot Set and Fractal Geometry.

Whether we look at incredibly large-scale things such as galactic clusters, and Galaxies; moderate scale such as cloud formations, river deltas, wind-blown dunes and coastal profiles; or small scale such as the edge of a leaf, the folds of the brain, the network of imtermingled neurons, the roots of a tree or the veins and arteries in flesh, we see something very like a fractal. Fractals are mathematical representations which repeat in an infinite regression of similar, but slightly different patterns. As you look closer and closer at the features of a fractal, you see what appears to be an endless regression of repeating symmetry. But how small can that scale go in reality? Photographs or prints of the Mandelbrot Set are limited in their fineness by the size of the grain in the photographic paper or the dots in the print. But how about nature? Are we dealing with something that has a lower limit set by the Planck Constant or some such, or does it indeed not stop, but proceed to infinity in some crossover between the material world of particles and the infinite beneath and beyond the material world?

If you can spare the time, (about 50 minutes for all 6) watch all 6 of the YouTube clips of Arthur C. Clarke’s Fractals. The movie doesn’t answer my question, although Stephen Hawking offers his informed opinion. In the end, it just asks the question in far more eloquently terms than I can put into words.
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I cannot tell you why. But after watching the 6 clips above, I just had to listen to Pink Floyd’s Shine on You Crazy Diamond, written as a tribute to their friend gone mad, Syd Barrett. I hadn’t listened to it in years, but somehow it congealed the Mandelbrot Set for me. If you know of a piece of music that works the same for you, I recommend it as a way to let the whole enormity of this Strange Universe sink in.

This is a continuation in the Strange Universe series.
1—How can the most distant quasar be 28 Billion light years away?
2—Can nothing exist without the Universe?
3—How can order emerge out of chaos?
4—Where is the center of the Universe?
5—If CERN proves there are parallel universes, will you move?
6—If the universe expands at faster than the speed of light, does it begin to go back in time?
7—What is the expanding universe expanding into?
8—Big Bang Theory—How can you divide infinity into a single finite whole?
9—How would you answer this speed-of-light question?
10—What happens when the expansion of the Universe reaches the speed of light?
11—What’s your Strange Universe example to illustrate Sir Arthur Eddington’s quote?