It seems to do pretty good at explaining the form of a snowflake, a salt crystal, diamonds...
For Lurkers, the original point raised by Sheldrake:
The mechanistic explanation of morphogenesis attempts to explain it in terms of molecules and interactions between them, particularly in terms of DNA and protein synthesis. This is a bottom-up approach, and can not explain the emergence of form. For example, genes code for the sequence of amino acids in proteins, but this can not even explain how the proteins fold up in the correct way to give the right three-dimensional structure.
Life, on the other hand, cannot be explained only by such external forces. Hence, the mathematicians have turned so often to self-organizing complexity. The emphasis is on the "self" as the article explains. Other types of complexity are also being investigated: Kolmogorov, physical complexity, functional complexity, metatransition, etc.
But as the just linked article suggests, the computational complexity is not enough to explain the emergence of life (v non-life/death). It also requires an investigation of information (successful communication), autonomy, semiosis and intelligence.
The "form" issue itself makes this point very clear on several levels. As Sheldrake mentions, the geometry of the DNA itself cannot be explained from the "bottoms up" mechanistic approach.
And then there is the "form" of the organism, such as the human body, which continues to exist as a "whole" even though every cell is replaced every seven years.
Likewise, the "form" of a collective of organisms - such as a colony of Army ants - exists only when the number of ants reaches a threshold. IOW, put 100 Army ants on a flat surface and they will walk in a circle until they die. But put a half million ants together and you have a "whole" which organizes raids, maintains geometry, schedules and acts collectively to benefit the whole.
Another point in "form" is the molecular machinery of an organism which organizes around a function to the benefit of the whole organism. Not only does the organism pursue life, but the molecular machinery as well. If the brain is dead, by attaching a respirator, the rest of the molecular machinery will pursue life.
In sum, life is characterized by purposeful form - or geometry - which cannot be explained by external, natural forces alone. That issue reaches beyond chemistry and biology into mathematics, physics and metaphysics, e.g. consciousness/mind/soul.
That stuff's impressive,
but I remind myself that
mimicking a form
may or may not say
fundamental things about
the main form itself.
Hundreds of years back,
when European painters
mastered oil painting
the combination
of smooth blending and knowledge
of perspective led
some folks to wonder
how powerful images
might be and the Church
of course got involved . . .
(And, of course, ancient sculptors
could get so good that
their work gave rise to
Pygmalion-type musings.)
So, the modern world
can take fractal math
and iterate shapes that look
like real world structures.
I can't figure out
if this is a deep statement
about how forms grow,
or if computers
and algorithms are just
our time's medium
the way the old Greeks
had sculpture or Europe had
really good painters.
After all, programs
only create ferns and stuff
because programmers
work creatively
to isolate and arrange
the fractal routines.
aquila48, indeed these things have form. But it is not the same kind of form that living systems have. For the instances you give are "informed" by relatively simple, repetitive instructions (information). In comparison, living organisms are astronomically more complex, and likely are not reducible to such simple repetitive instructions.
In short, a "bottom-up approach" from simple instructions/material basis -- which is available for the non-living systems you cite -- will likely not get you to an explanation or description of even the simplest of living forms, even supposing a hypothetical eternity for evolution.
FWIW, there is an important distinction to be made between "ordered" and "self-ordering systems" (crystals, snowflakes, dust eddies, tornadoes, Benard cells, etc.), and "self-organizing systems" (living organisms) in nature. WRT the latter, I do not think they "reduce" to the relatively low level of informational complexity that we observe in the former. For one thing, living states are constantly changing from moment to moment both at the organic level of the sytem and at the sub-levels (molecules, macromolecules, organelles, organs, etc.); for another, they are able to modify their paths from those predicted on the basis of initial conditions and the physical laws. They are "self-moving" and even "self-repairing" systems.
In other words, biological systems clearly have a physical/material basis; but they are not entirely reducible to the laws of physics and chemistry. There is something else involved in living systems that physics and chemistry cannot "access," let alone explain.
Or at least, that is my view, based on the present state of knowledge that I have. Which I guarantee you, is incomplete.
So, FWIW.... Thanks for writing!