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Fern leaves and cauliflower curds are not fractals (2012)

ncbi.nlm.nih.gov

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Re: Fern leaves and cauliflower curds are not fractals (2012)

#51

Post by [deleted] »

robotresearcher wrote: post #36
throwbadubadu wrote: post #5

> 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 mountain…

> 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 bifurc…

[deleted]

Re: Fern leaves and cauliflower curds are not fractals (2012)

#52

Post by robotresearcher »

JadeNB wrote: post #50
robotresearcher wrote: post #36

Earlier quoted context omitted.

> 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 bifurc…

> 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 l…

Crystals perhaps? Bottom up rather than top down, but locally recursive.

Re: Fern leaves and cauliflower curds are not fractals (2012)

#54

Post by mkaic »

A less prescriptivist title would be "I disagree with how people use the word fractal", as words are defined by how they're used and in what contexts, not by dictionaries or institutions. Considering that many, many people call fern leaves and cauliflower curds fractals, I see no issue with them continuing to do so. English as she is spoke.

Re: Fern leaves and cauliflower curds are not fractals (2012)

#56

Post by ska »

dekhn wrote: post #40
mfragin wrote: post #34

Earlier quoted context omitted.

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 i…

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.

> 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.

Re: Fern leaves and cauliflower curds are not fractals (2012)

#58

Post by ska »

franciscop wrote: post #26
throwbadubadu wrote: post #5

> 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 mountain…

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"

> "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.

Re: Fern leaves and cauliflower curds are not fractals (2012)

#59

Post by JadeNB »

robotresearcher wrote: post #52
JadeNB wrote: post #50

Earlier quoted context omitted.

> 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 l…

Crystals perhaps? Bottom up rather than top down, but locally recursive.

> Crystals perhaps? Bottom up rather than top down, but locally recursive.

Great example!

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