Fractal Features of Proto-Plant’s Origin and their Possible Consequences

The extension of the sectional model of the spruce crown’s dynamics into diapason (0, 1) of the fractal parameter μ has demonstrated the existence of green biomass on branches of three orders in form of photosynthesizing (green) points. We investigated the growth of point sets on an interval as a model of the origin of proto-plants, which are formed due to endosymbiosis of cyanobacteria and protists. The fractal properties of the sets of evenly placed points and group sets were studied using the box-counting method. For the group sets, the character of dependence μ on the growing total number of points changes radically differently depending on whether the number of the points per group or the number of groups was fixed. As the host does not have the initial infrastructure needed for an increase in cyanobacteria per group, the first path is implemented and μ decreases from 1 to 0.25 when groups consist of two points per group. If and when the host develops necessary anatomical features (infrastructure), the second pathway is realized and μ grows to 1. The combined trajectory of μ initially demonstrates a slow growth of the size of the photosynthetic system and then an exponential growth after the development of the host’s infrastructure. Similar fractal peculiarity also characterizes trees and is an innate property of plants. Assumptions on the morphological recapitulation of proto-plant in higher plants’ ontogenesis (embryogenesis and seed germination) and also a possibility to fix the number of cyanobacteria per group are discussed.