# What qualifies as science?

Perhaps this:
https://en.wikipedia.org/wiki/L-system

Question: are you looking for a form of bio-chemistry or a DNA code, which regulates the growth of fractal plants?
Even that is all about mathematics and then handwaving generalisations, with no mention of any specific biological mechanism that operates by a particular defined fractal algorithm.

Perhaps this:
https://en.wikipedia.org/wiki/L-system

Question: are you looking for a form of bio-chemistry or a DNA code, which regulates the growth of fractal plants?
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.

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Even that is all about mathematics and then handwaving generalisations, with no mention of any specific biological mechanism that operates by a particular defined fractal algorithm.
Is that not how we do science? With mathematics?

Fractal patterns are observable, mathematically describable, and testable. What more do you need?

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?

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Is that not how we do science? With mathematics?

Fractal patterns are observable, mathematically describable, and testable. What more do you need?
No. It is not.

In science, we tease out actual mechanisms, for specific individual phenomena, that operate by specific rules, expressed mathematically if we can do so.

I would therefore expect someone to study one specific growth process, in a specific organism, show what mechanism operates and put forward the exact algorithm (out of the billions that can be conceived of) that accounts for how it works.

Handwaving waffle, showing that some algorithms can generate something-that-looks-like-a-fern, does not cut it.

Drop all the artistic and abstract fractals, they are not pertinent to the subject except in the most abstract way.
Yet fractals are used throughout applied sciences, as well 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?

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?
Drop the rhetoric and learn how science works.

Drop the rhetoric and learn how science works.
Do you know how science works? Why don't you tell me?

I would therefore expect someone to study one specific growth process, in a specific organism, show what mechanism operates and put forward the exact algorithm (out of the billions that can be conceived of) that accounts for how it works.
Then why don't we take a specific fractal growth process in a specific organism and study its DNA coding which gives it its fractal properties?

But I believe Barnsley already did that. Did you even bother to read the link? You are the scientist, you should be able to make sense of the formal argument and the maths.

.

Research Article
Fractals and Hidden Symmetries in DNA
Carlo Cattani
Department of Pharmaceutical Sciences, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

The Influenza Virus.
Abstract
This paper deals with the digital complex representation of a DNA sequence and the analysis of existing correlations by wavelets. The symbolic DNA sequence is mapped into a nonlinear time series. By studying this time series the existence of fractal shapes and symmetries will be shown. At first step, the indicator matrix enables us to recognize some typical patterns of nucleotide distribution. The DNA sequence, of the influenza virus A (H1N1), is investigated by using the complex representation, together with the corresponding walks on DNA; in particular, it is shown that DNA walks are fractals. Finally, by using the wavelet analysis, the existence of symmetries is proven.
The main task of this paper is to show the existence of hidden geometries which underly the structure of a DNA sequence. Moreover, it will be shown that this geometry is fractal. In order to achieve this goal the fundamental steps are(1)the choice of the digital representation of the symbolic sequence of DNA,(2)the definition of the indicator matrix,(3)the construction of walks on DNA,(4)the cluster analysis of wavelet coefficients.
In this paper it will be shown that the distribution of nucleotides A, C, G, T along the sequence must fulfill some hidden geometrical rules, thus implying that the biological activity depends on these geometrical rules. The understanding of the underlying biological function from a possible interpretation of the given sequence of nucleotides [16] is still under investigation.
9. Conclusion
In this paper some fractal shapes and symmetries in DNA sequences and DNA walks have been shown and compared with random and deterministic complex series. DNA sequences are structured in such a way that there exists some fractal behavior which can be observed both on the correlation matrix and on the DNA walks. Wavelet analysis confirms by a symmetrical clustering of wavelet coefficients the existence of scale symmetries.
https://www.hindawi.com/journals/mpe/2010/507056/

Does this count as science?

The Fibonacci sequence is a limited fractal
No, it isn't.
You seem to have trouble here. Here:
https://www.quora.com/Is-the-Fibona...a-related-concept-thats-different-in-some-way
Is the Fibonacci sequence a fractal - -
- - -
Sigurd Wenner, Condensed matter physicist
Updated Mar 17 2013
- - - -
To the main question, the answer is no. The Fibonacci sequence can be used to create some nice visuals like the Golden spiral, and probably some geometric entities with fractal nature. But the sequence of numbers itself is not a fractal.
Fractals are used throughout applied sciences,
So are circles and triangles
and exist throughout the entire universe.
No, they don't. Neither do circles and triangles.
Then why don't we take a specific fractal growth process in a specific organism and study its DNA coding which gives it its fractal properties?

But I believe Barnsley already did that.
He did not demonstrate even whether the DNA coding was responsible for the fractal-approximating growth habit - any of it.
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.
Not the "how and why" - it specifically refers to that as a speculation, in your link.

Does this count as science?
If it demonstrates that a fractal exists in nature, why would it matter whether it's science or not?
Some of the terminology in the paper seems to be above my level. Can you describe in simple terms what exactly is a fractal, according to that paper?

Write4U said:
Fractals are used throughout applied sciences,
Iceaura said;
So are circles and triangles
Write4U said; and exist throughout the entire universe.
Iceaura said;No, they don't. Neither do circles and triangles.
Write4U said:
Does this count as science?
NotEinstein said;
If it demonstrates that a fractal exists in nature, why would it matter whether it's science or not?
Knowledge? Survival?
NotEinstein said;
Some of the terminology in the paper seems to be above my level. Can you describe in simple terms what exactly is a fractal, according to that paper?

I'll let this link speak for me.

---------Euclidean geometry-------------------------|-----------------Fractal geometry------------------

For us nature coders, we have to ask the question: Can we describe our world with Euclidean geometry? The LCD screen I’m staring at right now sure looks like a rectangle. And the plum I ate this morning is circular. But what if I were to look further, and consider the trees that line the street, the leaves that hang off those trees, the lightning from last night’s thunderstorm, the cauliflower I ate for dinner, the blood vessels in my body, and the mountains and coastlines that cover land beyond New York City?
Most of the stuff you find in nature cannot be described by the idealized geometrical forms of Euclidean geometry. So if we want to start building computational designs with patterns beyond the simple shapes ellipse(), rect [], and line/, it’s time for us to learn about the concepts behind and techniques for simulating the geometry of nature: fractals.
8.1 What Is a Fractal?
The term fractal (from the Latin fractus, meaning “broken”) was coined by the mathematician Benoit Mandelbrot in 1975. In his seminal work “The Fractal Geometry of Nature,” he defines a fractal as “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole.”[/quote]

http://natureofcode.com/book/chapter-8-fractals/

I cannot do better than that, so you'll have to read the link.

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I cannot do better than that, so you'll have to read the link
Your link seems to have nothing to do with your arguments here, and it deals with none of the issues raised in the posts you quoted.

Knowledge? Survival?
Naming arbitrary things is not an answer. Let's say the paper is scientific: that doesn't mean it's using the word fractal correctly. If the paper isn't scientific, that doesn't mean it's using the word fractal correctly.
One is unrelated to another (although one might expect better from the former). Just like "survival" is unrelated. And for "knowledge": that's what's up for debate.

I'll let this link speak for me.

I cannot do better than that, so you'll have to read the link.
I should have specified: what are "shapes and symmetries in DNA sequences"?
What are "DNA walks"?
What is a "time serie"?
What are wavelet coefficients, and what is "the cluster analysis of wavelet coefficients"?

Naming arbitrary things is not an answer. Let's say the paper is scientific: that doesn't mean it's using the word fractal correctly. If the paper isn't scientific, that doesn't mean it's using the word fractal correctly.
Neither does it mean that it's using the word fractal incorrectly.
One is unrelated to another (although one might expect better from the former). Just like "survival" is unrelated. And for "knowledge": that's what's up for debate.
Knowledge is the aim of science, no? Natural selection of specific traits seems to be important for survival and procreation, no?
I should have specified: what are "shapes and symmetries in DNA sequences"?
Perhaps this (looks fractal to me);

The genetic code had to be a "language" — using the DNA alphabet of A, T, C, and G — that produced enough DNA "words" to specify each of the 20 known amino acids. Simple math showed that only 16 words are possible from a two-letter combination, but a three-letter code produces 64 words.
What are "DNA walks"?
No clue
What is a "time serie"?
No clue
What are wavelet coefficients, and what is "the cluster analysis of wavelet coefficients"?
No clue.

I'll leave all those questions for you to pursue on your own.
If I have peaked your interest, then I am satisfied with my contribution to this discussion.

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Neither does it mean that it's using the word fractal incorrectly.
So we agree that your question was totally irrelevant.

Knowledge is the aim of science, no?
Sure, that's why we are debating if "fractals exist in nature" is knowledge (i.e. truth) or not.

Natural selection of specific traits seems to be important for survival and procreation, no?
What does this has to do with anything?

Perhaps this;

That's (a rendering of a part of) a DNA-molecule, not a DNA sequence.

No clue No clue No clue.
In other words: you have no idea what the paper is about. How can you judge its merits then?

I'll leave all those to you to pursue on your own.
In other words: you aren't even going to bother trying to find out whether this paper is worth anything. Then I can dismiss the paper just as easily.

If I have peaked your interest, then I am satisfied with my contribution to this discussion.
You have posted a link to a paper, and now you show you don't even understand its terminology. I think that's called "being off-topic", not "contributing to this discussion".

Carry on ...........

Do you know how science works? Why don't you tell me?

Then why don't we take a specific fractal growth process in a specific organism and study its DNA coding which gives it its fractal properties?

But I believe Barnsley already did that. Did you even bother to read the link? You are the scientist, you should be able to make sense of the formal argument and the maths.

.

Of course I read the link. But that link was almost entirely abstract mathematics. The only observation referred to was - indirectly - that of the growth of algal populations, and even for that no experiment or other observations had been done and no actual quantitative model of an actual experimentally observed population had been verified. This is the same with just about every other description of fractals in nature that I have come across. Lots of pretty pictures and arguments in principle, but no quantitative modelling of actual systems. It is undeniable that natural growth processes seem to follow fractal-like, iterative steps and result in very similar patterns, but there does not seem to be much, if anything, in terms of specific quantitive modelling of specific, experimentally observed processes. I found a more persuasive explanation of the power and limitations of fractal analysis in plant growth here: http://algorithmicbotany.org/papers/abop/abop-ch8.pdf No need to read all the maths but the summary at the end is worth reading I think.

I continue to get the strong impression that there are fairly few techniques in science , even in biology where it is most obviously applicable, that rely on fractal mathematics to make predictive models of natural behaviour. Frankly, fractals, after all the hype (they do look so pretty and "organic" to journalists, after all) , appear to me to be something of a disappointment. I'd love someone more knowledgeable to show that I am wrong, because they are very seductively beautiful.

As for "Why don't you tell me" how science works, what do you think I have been telling you in the last few posts? Did you bother to read post 785 for instance? There is a limit to how often you can expect me to repeat myself.

P.S. the opening of the link nicely makes the point that these fractal representations are approximations, not true fractals, due to their finite range of scales. This is exactly what Not Einstein and Iceaura have been telling you.

Thank you for that informative link.....

Thank you for that informative link.....
Good. I highly recommend that you read, mark, learn and inwardly digest the first and last paras. They give what seem to me helpfully accurate and concise statements of (1) how fractals can only approximately mimic natural forms and (2) the limitations and assumptions implicit in trying to use them to model biological structures.