What have fractal life forms with numerically generated fractals in common ?

[GabiM]

Basically, there are interferences (in time).
Numerical values that have been changed in one or a few iterations must again swing in the other direction.
(It's like extinction when compared with light intensities at spatial overlay.)
Here, earlier figures ("random") again achieved - then there is a cycle.
However, much depends on the number length (number of digits).

Here again the question: how many digits iterated nature?

Because of the Fibonacci series, it could be that three suffice.
Two buds are superimposed by adding the fields, and at the maximum the third bud grows. For the fourth bud, the first bud has no influence.
She's too far away.
Are usually 3 generations in our lives there at the same time, the influence each other, not 5 or 10 .

The iterations are but no waves, but rather something other than interference cancellation.
On the other hand defines Z = R * e ^ (i * w) ----- ------------ plane waves are so you just have to have imagination.

That's why I would not say that iterations are less complex than waves, but they are MORE complex.
A fixed point would be the wave solution: A single frequency w with amplitude R.
--------- For dynamic behavior rather boring. Dead.

Nature:

A total fixed heart rate is abnormal.
Sharp frequencies are very unhealthy when you're exposed to.
Therapy equipment specially put other waves over it (on their operating frequency), modulate with Schumann wave, and what else has said the planet as a vibration.

Much takes place in the unit circle, which is like a mirror.
An interferometer is also not without a mirror.
Phase boundaries and temperature stratification can be like mirror.
Cell walls are  nothing else.

Nature has also other ideas:
Vortex with sub-vortices. Curvature instead mirroring.
Adjacent fluidized beds may overlap also.
This leads to the variable quantization. Quantum are vortices.

If we dots or shapes in the fractals found, the number of movement forms a stable vortex, we have recognized the iteration in nature.

[DarkBeam]

Interesting ideas even if the discussion is not easy to follow

[bib]

Raw mathematical fractals and natural fractals can be compared on two different and nested levels : a fundamental one, and a visible one. In biology, I would call the first level structural and abstract, related to the complexity created by the replication of the DNA molecule, the duplication of the genetic messengers' information consisting of only four characters (ATGC), a few simple rules set that can create the diversity and the beauty of life. Life is an information science that creates complexity and wonders through a relatively small set of simple instructions, and letting time do its work. The parallel is obvious with fractals which are a branch of mathematics creating complexity and wonders through a relatively simple algorithm and lots of patience. The second level is the visible, tangible, three-dimensional one, that we see in trees and cauliflowers. Besides Maths and Biology, I would also add Arts in the equation. The theoretical vision is translated into practice by the feeling provided by the creation of fractal art. Indeed, fractal art is largely based on an activity of modeling algorithms and mathematical formulas via computers. The purpose of this activity is to generate fractal images (in 2 or 3 dimensions), images thus sharing a common origin, a common DNA if you wish, with the aforementionned two levels of fractality : first the initial creative power of the universe gives rise to increasing complexity, which is a fundamental characteristic of the dynamics of fractal art, and secondly its tangible and visible manifestation through all objects and observable fractal phenomena around us in nature, life, and even in our own body.

[stereoman]

  To me,   Between a natural fractal and a computer simulation, there is the same difference we find between a real person and a sculpture of the same person.
             What they have in common?, External aspects, inside they are quite different.
              But it is true that it takes three terms to anything to be possible, so the three is a sacred number
             This is the Active Force, the Passive Force, and the Balancing force, namely, Expansion, Contraction and Rotation.
              This three terms are found in the chemicals, in the form of acids, bases and salts,  in the three primary colors of the spectrum, is the triangle and the tetrahedron in geometry, and so on.
               Also, that´s why we live in a three-dimensional world.

[cKleinhuis]

             This is the Active Force, the Passive Force, and the Balancing force, namely, Expansion, Contraction and Rotation.
             

make it scaling, rotating and translating you have got the mandelbrot transforms