You can see the basic issue even confined within the mathematics. Look at "Example 5" in your link, where a given fractal (the Sierpinski Triangle) has at least two fundamentally different generating algorithms, producing successive approximations that in their first few iterations (and therefore at all sufficiently small scales) do not closely resemble each other let alone the fractal limit.

Whatever the Sierpinski Triangle is an "expression" of is not specified by the Triangle itself, and any given Sierpinski Triangle of unknown origin cannot be assumed to have been the "expression" of any given algorithm - even one that would work.

If one expands attention to physical manifestations of approximate S Triangles, finite objects that seem in some way to be tending toward that fractal, the situation is worse yet: now generating algorithms that in their limits do not produce fractals at all must be considered.

Drop all the artistic and abstract fractals, they are not pertinent to the subject except in the most abstract way. Fractals are not things, they are mathematical sequences. They can have beginnings and they can have physical limits (ends).

Fractals are used throughout applied sciences, and exist throughout the entire universe.

The Fibonacci sequence is a

**limited** fractal found throughout nature. Nowhere does it say that the Fibonacci sequence

** must **be extended into infinity. In nature it is just an evolved formula with a start point and an endpoint. "Phi" and the "Golden Ratio" are just imaginary patterns, which have no application in nature?

What about Pi? Its a number which can extend infinitely without a repeating pattern. It appears in nature and we use it almost everywhere. You don't even need a circle to calculate Pi. How then is that possible?

Look at Barnsley and the "L" system, which deal specifically with fractals as found in biological systems. It specifically mentions DNA coding and how and why these fractal properties emerge as specific growth patterns.

I gave the links, which look pretty scientific to me, including the maths.

Are these people not scientists performing science? All of the sciences (our understanding of how and why things work) depend on the maths we can apply to them.

By your standards nothing is science. Might as well sit back and enjoy the view.

Tell me what you would consider science in biology. You tell me to look up definitions in Wiki, and when I do you tell me Wiki is wrong in some areas.

Is biology a scientific disciple or not? If it is, where is the science part? If not, should I start praying for miracles?