Many biological organisms -- such as trees, broccoli, and the blood vessels in animals -- can be approximately described using fractals.
What is the reason behind such fractals? Specifically, do we know of the way certain cells split that lead to fractals? Do we know if there are specific genes that tend to generate fractals?
because fractals are emergent structures created by simple rules, as are many biological structures. The same kind of simple recursive signals that lead to fractals are simple enough to be stumbled on by biological evolution and are effective ways to deal with the scaling problems created by the square cube law.
Essentially, eukariote cells use internal and external signalling hormones, so the cells can have a front/back/top/bottom end and can orient themselves at specific angles using signalling hormones, which also travel outwards through chains of cells and form signalling hormone concentration gradients. Eventually, when the gradient reaches a certain level, it can cause a distant cells to divide in two resart the gradient, so that very precise distances can grow using very precise angles.
The research on genetics related to the dendritic morphogenisis in trees, neurons, lungs, ferns and other forms in nature, doesn't give a clear summary of the process that you thought it can.
There was a patent of a technology called "Fractogene" quoted by some serious research, and doesn't involve coherent propositions and sentences! if you can figure out what FractoGene was, please comment!
You'll find talk about P-cells, Cytoskeletons, Drosphila, Danio, meristems, concluding:
We expect that a new generation of data mining tools will be required to support recursive fractal geometrical, combinatorial, and neural network models of the genomic basis of morphogenesis.
A fractal can be written in 3 instructions (copy, advance, divide) so the cells only have to have 3 behaviours to create a fractal, it's very simple. Even H2O and NaCl can form dendrites similar to plant roots, so fractal genes have an fairly simple basis.
Dendritic gold:
dendritic copper:
dendritic manganese oxides on limestone:
Even pure water forms branches similar to trees. Something so simple to generate in nature is likely to have parallel evolution of many thousands or millions of genes that regulate the precise shapes of the fractals in many organisms.
What kinds of signalling hormone gradients and genes regulate branch and leaf vein angles are very obscure and I didn't find much about "branch angle gene regulation".
You'll find information like: "The plant hormones cytokinin, auxin and gibberellin are crucial during root development." cool description of plant hormones
Here's the best read I found on the subject: https://dev.biologists.org/content/147/10/dev184499
The most confusing to read: https://pubmed.ncbi.nlm.nih.gov/16527761/
I scanned through 15 research papers and very few claim to have found the mechanisms that regulate the morphogenesis of fractals in the natural world.
Firstly, it is necessary to note that fractals are not unique to live things: for example, a seashore is an example of fractal structure (with theoretically infinite length).
In regard to trees and broccoli, it is necessary to note that fractal structure maximizes the area, given the same volume, as opposed to other shapes (e.g., a spherical organism would have most of its cells inside the sphere), thus increasing the area exposed to sun and facilitating photosynthesis. As such, having such a shape increases the fitness of the organism, and almost certainly is encoded genetically as the result of natural selection. For example, see here.
Let me also bring the attention to the fact that fractals occur also on single-cell levels, such as the dendrites of a neuron.
Update
Fractals are more ubiquitous in live nature than it may seem at the first glance. The obvious examples are the shapes of trees, vascular systems (of trees and animals), neural networks, etc. Less obvious examples (because of being somewhat abstract) are metabolic networks, community food network patterns, and possibly ecen evolutionary patterns (depending on whether we believe that evolution has explored all the possibilities).
West an co-workers have used fractals to explain the scaling laws relating many biological quantities, e.g., such as basal metabolic rate and the lass or organism $$ Y=Y_0M^{b}, b=\frac{3}{4} $$ See here for general review and the references, but also the references by @John in the other answer. While purely geometric arguments would imply scaling laws proportional to $b\propto 1/3$ (since volume scales as length to the thirs power), the fractal nature of these networks allows to infer the correct exponents, $b\propto 1/4$.
The theory by West et al., is based on three assumptions:
The third assumption, maximization of energy, is essentially the requirement of the maximum fitness. What appears to be somewhat fo an open question is to what extent the the living organisms evolve towards fractal structures or whether it is characteristic of all the living organisms, inherited from the most recent common ancestor.
