hmm, the graph kinda reminds me of a positive and negative feedback loops, although im almost certain that that isnt being discussed here
anyhow fractals dont technicly require imaginary number if you're using ratios...
take for example a spiral, one which is spiraling in at a half it's length every half turn, so it would start at like 4, then the next segment would be 2, 1, .5, .25, etc, on and on...
or some sort of branching could also be a fractal, say you have a line that branches once 1/2 it's length, and branches again where it ends, and each of those react likewise to the original line
This also in a way can work with molecules. Although it very a primitive example of a fractal but the way molcules lump (especially carbon, etc.) can express fractals. Even with DNA, every 2.34 AT or CG connections (the ladder rungs) the double helix rotates a half turn i believe... so there are definitely ways to express fractals without having to consciously dip into imaginary numbers.