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> Actual fern leaves and cauliflower curds have a very small number of anatomically variable and non-iterating bifurcations, which superficially look self-simil

> Actual fern leaves and cauliflower curds have a very small number of anatomically variable and non-iterating bifurcations, which superficially look self-similar, but do not allow for scaling down of their structure as real fractals do. Sorry, can't help it, but really? You cannot zoom into real-life fractals infinitely like in those math animations, only a few times? What comes next? Even the coast line or mountains fractal analogies are wrong in the mathematical sense, you won't even the same shape once if you try hard?? > The above cases demonstrate a general problem of using mathematical tools to investigate or illustrate biological phenomena in an irrelevant manner. No, I think we have a different problem here..

bannedbybros 3y ago
[dead]
LesZedCB 3y ago
imagine publishing a whole paper to win an "Um, actually" argument
ajuc 3y ago
Fractals don't even need to be self-similar. They just need to have fractal dimension (if you double the size of every feature - the exponent near the scaling factor must be non-integer). Self-similarity is the easiest way to make a fractal, but not the only one. In fact the idea of fractal was invented for real-life non-self-similar objects. The simple self-similar ones are just examples that are easiest to understand.
- ouid 3y ago
  As far as i can tell, fractal doesn't have a definition. The closest it ever came was the one you roughly gave.
  - idiotsecant 3y ago
    https://en.wikipedia.org/wiki/Fractal_dimension https://en.wikipedia.org/wiki/Fractal_dimension Not only are fractals very well defined in mathematical terms, but there are further mathematics based on those definitions.
    - ouid 3y ago
      From the article you linked: >Ultimately, the term fractal dimension became the phrase with which Mandelbrot himself became most comfortable with respect to encapsulating the meaning of the word fractal, a term he created. After several iterations over years, Mandelbrot settled on this use of the language: "...to use fractal without a pedantic definition, to use fractal dimension as a generic term applicable to all the variants."
  - _a_a_a_ 3y ago
    https://html.duckduckgo.com/html?q=fractal%20definition https://html.duckduckgo.com/html?q=fractal%20definition did you even look?
- mfragin 3y ago
  When I was teaching math and comp sci, I used broccoli in an example to explain self-similarity: imagine you're playing with your Barbies or GI Joes and you want to make their dinner plates look like they have real food on them. You can break off a much smaller piece of broccoli and it will look "to scale" on the plate. Try that with a banana! That was to explain the concept of self-similarity, something we CAN see in fractals. Note: for anyone wanting an easy way to experiment with L-systems, there's a built-in feature in Inkscape that is pretty fun to use. It's under "Extensions/Render/L-System"
  - dekhn 3y ago
    I don't perceive broccoli as self-similar at any scale (maybe I'm missing something), but romanesco, for sure. I see at least 3 levels of self-similarity.
    - ska 3y ago
      > maybe I'm missing something I think you are. At the very least, you can clearly break a piece off a floret to resemble a scaled version of the whole head.
- michaelcampbell 3y ago
  Thanks, this and the post to which you replied taught me something that I did not know. TIL...
sfvisser 3y ago
Agreed. I’m not a biologist, but I always assumed the self similarity of plants and trees is definitely some recursive process with some boundary conditions or external constraints as an implicit parametrization. Which is very similar to how you can describe (some) fractals. It feels very unlikely to me that the tree dna for thick branches is completely different from that for thin twigs.
- EamonnMR 3y ago
  The thick branches, of course, start out as thin twigs.
- RosanaAnaDana 3y ago
  It's really not that complicated. all vascular plants have basically the same node -- axially meristem -- internode -- node pattern to growth. All plants are actually fractals but it's not a long the leaf dimension, it's along the stem axis. It's also why it's so easy to effectively take cuttings and get a an 'fully mature' plant from them (eventually). Every node--etc.. section is the same pattern as every other. It's largely due to the exogenous origin of branching.
  - robotresearcher 3y ago
    > All plants are actually fractals but it's not a long the leaf dimension, it's along the stem axis. > Every node--etc.. section is the same pattern as every other. Common sense says this isn't true. Some sections grow leaves and flowers rather than smaller branches, others do not.
    - ksaj 3y ago
      It boils down to an if statement. Once you've reached a certain number of iterations, or the initial branching meets certain conditions, another rule set applies. But those rules are still not all that different - follow the leaf veins, and all their branching throughout. The same applies to the roots.
franciscop 3y ago
Next comes this: > "The fern leaf thus develops from the inside out and not by randomly dispersed dots that gradually fill the leaf area, as is done with chaos computer programs." Yeah, real life is not a computer simulation (AFAIK), and thus is not made "of randomly dispersed dots"
- eternalban 3y ago
  They were referring to this distinction: "Organic form itself is found, mathematically speaking, to be a function of time.... We might call the form of an organism an event in space-time, and not merely a configuration in space." - D'ary Thompson https://en.wikipedia.org/wiki/D%27Arcy_Wentworth_Thompson https://en.wikipedia.org/wiki/D%27Arcy_Wentworth_Thompson https://en.wikipedia.org/wiki/On_Growth_and_Form https://en.wikipedia.org/wiki/On_Growth_and_Form
  - anigbrowl 3y ago
    This may be true even for inorganic matter, eg cracks in dried mud follow a predictable development that can be modeled quite economically. http://irep.ntu.ac.uk/id/eprint/28373/1/5915_Goehring.pdf http://irep.ntu.ac.uk/id/eprint/28373/1/5915_Goehring.pdf
- ska 3y ago
  > "The fern leaf thus develops from the inside out and not by randomly dispersed dots that gradually fill the leaf area, as is done with chaos computer programs." That one is kind of silly, because while the chaos game is one way to realize an IFS like the Barnsley fern, there are others that are more geometric. For example specifically in that case, you can iterate any closed set in the plane under the contractive mapping that defines it, and you will end up converging to the set. Nothing chaotic about that. The algorithm they are referring to (chaos game) does it pointwise which is easier in a computer, but relies on the fact that the resultant sequence of points will, at least after a while, stay distributed over a probability measure supported by the set.
robotresearcher 3y ago
> You cannot zoom into real-life fractals infinitely like in those math animations, only a few times? The point of the paper is that these are not 'real life fractals', so your correct declaration about the obviousness of real life fractals being bounded in their depth is not relevant, and does not make this paper pointless. It's not obvious to me that fern branches are 'anatomically variable and non-iterating bifurcations', rather than a recursive process that bottoms out at a size boundary. Now I know.
- JadeNB 3y ago
  > It's not obvious to me that fern branches are 'anatomically variable and non-iterating bifurcations', rather than a recursive process that bottoms out at a size boundary. But hardly any (no?) real-life phenomena are the latter! As a mathematician, I'm as bothered by imprecise use of mathematical terminology as anyone, but, if we're going to call anything in real life a fractal, then it surely means something more like "appears to contain structure at multiple scales" than "the same structure at all scales". As @throwbadubadu points out (https://news.ycombinator.com/item?id=35903049 https://news.ycombinator.com/item?id=35903049), the classical example of a coast-line will also have different structure at small scales and at large ones, so either we throw out calling that a fractal (OK with me!), or we accept that we're using precise language imprecisely.
  - robotresearcher 3y ago
    Crystals perhaps? Bottom up rather than top down, but locally recursive.
    - JadeNB 3y ago
      > Crystals perhaps? Bottom up rather than top down, but locally recursive. Great example!
  - CoolGuySteve 3y ago
    There were fractal body plans in the precambrian era but they went extinct pretty quickly. https://en.wikipedia.org/wiki/Rangeomorph https://en.wikipedia.org/wiki/Rangeomorph
CoolGuySteve 3y ago
That may be true but there were lifeforms with more fractal structures like the precambrian Charnia (https://en.wikipedia.org/wiki/Charnia https://en.wikipedia.org/wiki/Charnia ) and other Rangeomorphs ( https://en.wikipedia.org/wiki/Rangeomorph https://en.wikipedia.org/wiki/Rangeomorph ). The main difference the author is getting at (I suspect, I'm not a biologist) is that these earlier life forms display a multilevel fractal self-similarity within their fronds, basically fronds of fronds of fronds of fronds, instead of modern plants where the fronds have structural differences like leaves/buds that keep the pattern from replicating past a certain point. The weird thing is that as far as body plans go, a fractal shape would maximize surface area while minimizing body volume which would seem advantageous for a filter feeding organism. It's not clear why such a simple design went extinct so quickly.

bannedbybros 3y ago

[dead]

LesZedCB 3y ago

imagine publishing a whole paper to win an "Um, actually" argument

ajuc 3y ago

Fractals don't even need to be self-similar. They just need to have fractal dimension (if you double the size of every feature - the exponent near the scaling factor must be non-integer). Self-similarity is the easiest way to make a fractal, but not the only one. In fact the idea of fractal was invented for real-life non-self-similar objects. The simple self-similar ones are just examples that are easiest to understand.

ouid 3y ago
As far as i can tell, fractal doesn't have a definition. The closest it ever came was the one you roughly gave.
- idiotsecant 3y ago
  https://en.wikipedia.org/wiki/Fractal_dimension https://en.wikipedia.org/wiki/Fractal_dimension Not only are fractals very well defined in mathematical terms, but there are further mathematics based on those definitions.
  - ouid 3y ago
    From the article you linked: >Ultimately, the term fractal dimension became the phrase with which Mandelbrot himself became most comfortable with respect to encapsulating the meaning of the word fractal, a term he created. After several iterations over years, Mandelbrot settled on this use of the language: "...to use fractal without a pedantic definition, to use fractal dimension as a generic term applicable to all the variants."
- _a_a_a_ 3y ago
  https://html.duckduckgo.com/html?q=fractal%20definition https://html.duckduckgo.com/html?q=fractal%20definition did you even look?
mfragin 3y ago
When I was teaching math and comp sci, I used broccoli in an example to explain self-similarity: imagine you're playing with your Barbies or GI Joes and you want to make their dinner plates look like they have real food on them. You can break off a much smaller piece of broccoli and it will look "to scale" on the plate. Try that with a banana! That was to explain the concept of self-similarity, something we CAN see in fractals. Note: for anyone wanting an easy way to experiment with L-systems, there's a built-in feature in Inkscape that is pretty fun to use. It's under "Extensions/Render/L-System"
- dekhn 3y ago
  I don't perceive broccoli as self-similar at any scale (maybe I'm missing something), but romanesco, for sure. I see at least 3 levels of self-similarity.
  - ska 3y ago
    > maybe I'm missing something I think you are. At the very least, you can clearly break a piece off a floret to resemble a scaled version of the whole head.
michaelcampbell 3y ago
Thanks, this and the post to which you replied taught me something that I did not know. TIL...

sfvisser 3y ago

Agreed. I’m not a biologist, but I always assumed the self similarity of plants and trees is definitely some recursive process with some boundary conditions or external constraints as an implicit parametrization. Which is very similar to how you can describe (some) fractals. It feels very unlikely to me that the tree dna for thick branches is completely different from that for thin twigs.

EamonnMR 3y ago
The thick branches, of course, start out as thin twigs.
RosanaAnaDana 3y ago
It's really not that complicated. all vascular plants have basically the same node -- axially meristem -- internode -- node pattern to growth. All plants are actually fractals but it's not a long the leaf dimension, it's along the stem axis. It's also why it's so easy to effectively take cuttings and get a an 'fully mature' plant from them (eventually). Every node--etc.. section is the same pattern as every other. It's largely due to the exogenous origin of branching.
- robotresearcher 3y ago
  > All plants are actually fractals but it's not a long the leaf dimension, it's along the stem axis. > Every node--etc.. section is the same pattern as every other. Common sense says this isn't true. Some sections grow leaves and flowers rather than smaller branches, others do not.
  - ksaj 3y ago
    It boils down to an if statement. Once you've reached a certain number of iterations, or the initial branching meets certain conditions, another rule set applies. But those rules are still not all that different - follow the leaf veins, and all their branching throughout. The same applies to the roots.

franciscop 3y ago

Next comes this: > "The fern leaf thus develops from the inside out and not by randomly dispersed dots that gradually fill the leaf area, as is done with chaos computer programs." Yeah, real life is not a computer simulation (AFAIK), and thus is not made "of randomly dispersed dots"

eternalban 3y ago
They were referring to this distinction: "Organic form itself is found, mathematically speaking, to be a function of time.... We might call the form of an organism an event in space-time, and not merely a configuration in space." - D'ary Thompson https://en.wikipedia.org/wiki/D%27Arcy_Wentworth_Thompson https://en.wikipedia.org/wiki/D%27Arcy_Wentworth_Thompson https://en.wikipedia.org/wiki/On_Growth_and_Form https://en.wikipedia.org/wiki/On_Growth_and_Form
- anigbrowl 3y ago
  This may be true even for inorganic matter, eg cracks in dried mud follow a predictable development that can be modeled quite economically. http://irep.ntu.ac.uk/id/eprint/28373/1/5915_Goehring.pdf http://irep.ntu.ac.uk/id/eprint/28373/1/5915_Goehring.pdf
ska 3y ago
> "The fern leaf thus develops from the inside out and not by randomly dispersed dots that gradually fill the leaf area, as is done with chaos computer programs." That one is kind of silly, because while the chaos game is one way to realize an IFS like the Barnsley fern, there are others that are more geometric. For example specifically in that case, you can iterate any closed set in the plane under the contractive mapping that defines it, and you will end up converging to the set. Nothing chaotic about that. The algorithm they are referring to (chaos game) does it pointwise which is easier in a computer, but relies on the fact that the resultant sequence of points will, at least after a while, stay distributed over a probability measure supported by the set.

robotresearcher 3y ago

> You cannot zoom into real-life fractals infinitely like in those math animations, only a few times? The point of the paper is that these are not 'real life fractals', so your correct declaration about the obviousness of real life fractals being bounded in their depth is not relevant, and does not make this paper pointless. It's not obvious to me that fern branches are 'anatomically variable and non-iterating bifurcations', rather than a recursive process that bottoms out at a size boundary. Now I know.

JadeNB 3y ago
> It's not obvious to me that fern branches are 'anatomically variable and non-iterating bifurcations', rather than a recursive process that bottoms out at a size boundary. But hardly any (no?) real-life phenomena are the latter! As a mathematician, I'm as bothered by imprecise use of mathematical terminology as anyone, but, if we're going to call anything in real life a fractal, then it surely means something more like "appears to contain structure at multiple scales" than "the same structure at all scales". As @throwbadubadu points out (https://news.ycombinator.com/item?id=35903049 https://news.ycombinator.com/item?id=35903049), the classical example of a coast-line will also have different structure at small scales and at large ones, so either we throw out calling that a fractal (OK with me!), or we accept that we're using precise language imprecisely.
- robotresearcher 3y ago
  Crystals perhaps? Bottom up rather than top down, but locally recursive.
  - JadeNB 3y ago
    > Crystals perhaps? Bottom up rather than top down, but locally recursive. Great example!
- CoolGuySteve 3y ago
  There were fractal body plans in the precambrian era but they went extinct pretty quickly. https://en.wikipedia.org/wiki/Rangeomorph https://en.wikipedia.org/wiki/Rangeomorph

CoolGuySteve 3y ago

That may be true but there were lifeforms with more fractal structures like the precambrian Charnia (https://en.wikipedia.org/wiki/Charnia https://en.wikipedia.org/wiki/Charnia ) and other Rangeomorphs ( https://en.wikipedia.org/wiki/Rangeomorph https://en.wikipedia.org/wiki/Rangeomorph ). The main difference the author is getting at (I suspect, I'm not a biologist) is that these earlier life forms display a multilevel fractal self-similarity within their fronds, basically fronds of fronds of fronds of fronds, instead of modern plants where the fronds have structural differences like leaves/buds that keep the pattern from replicating past a certain point. The weird thing is that as far as body plans go, a fractal shape would maximize surface area while minimizing body volume which would seem advantageous for a filter feeding organism. It's not clear why such a simple design went extinct so quickly.