The humble C. elegans (roundworm) has ~20000 genes, similar to humans.
The complexity comes with the regulation of these genes, which are in the noncoding regions of DNA.
You can regulate the genes to "disable" the complexity, but those genes need to be there in the first place....
Functional diversity of the same gene can be generated through context-specific regulator-to-promoter interactions.
1) The amount of DNA does not determine the complexity of an organism.
2) Also, the number of protein-coding genes does not determine the complexity of an organism.
You may have meant (2), and only (2). If so, this is clearly true, as much of the complexity comes from non-protein DNA.
Still, (1) is also true, but one could argue, more due to random inefficiencies, or alternatively if you rank degree of complexity based only on phenotypes.
My preferred definition of complexity, or rather of irreducible complexity, is to say that complexity is determined by the minimum number of bits of information that is needed to create an equivalent output. (where, naturally, the definition of equivalence needs to be supplied for a given domain)
By this definition, DNA length (not number of genes) places an upper bound on complexity an organism can have.
To take the NN example:
Clearly it applies to species, like humans, with a significant cultural and learning element to our being. Much of our complexity is learned socially or by interacting with our environment. In fact, this is done by training the NN in our brains.
Edit: Note that our brains can store much more information than our DNA, making the upper bound on complexity for a human the sum of storage capacity in the DNA + the sum of storage capacity in the brain.
But for species with little ability to learn, like jellyfish, wouldn't it be more appropriate to say that the "training of the NN" is analogous to evolution optimizing the DNA? That would mean that, for a given individual, their complexity is all included in their DNA at birth?
In that case, one could argue that the length of the DNA string does create an upper bound on how much complexity it can contain. I suppose that is the case for the NN, too. The total number of bits in the weights of the network is an upper bound on the complexity a given, already trained, network can have. (Of course, the possible complexity of the network is way, way higher than that of the program that creates it.)
While the digits in Pi appear like white noise, fractals have a very distinct sense of orderliness, but with infinite detail. The latter tends to be more fascinating for most people.
Technically, the first is called disorganized complexity and the second organized complexity.
Sorry, but can you point any source please supporting your statement?