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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)

#3
> A realistic set of mathematical equations to describe fern leaf or cauliflower curd development is needed

I wish the author had derived these equations -- something like the book The Geometry of Pasta

https://www.amazon.com/Geometry-Pasta-Caz-Hildebrand/dp/1594...

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

#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 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..

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

#6
"Like fern leaves or any other plant branching system at the organ level, the cauliflower curd develops from the inside out through a process totally different from fractal drawing."

Soooo, what the author is stating is they are actually even more amazing and wonderfully made than we originally thought. Even though they look like the mathematical model of a built fractal they grow entirely different and with an internal program that cannot be reproduced by our existing knowledge-base.

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

#8
> A realistic set of mathematical equations to describe fern leaf or cauliflower curd development is needed

Well if we're talking about Lindenmayer's work on L-Systems being limited to abstract representations of plants, without getting into all the other structures we're seeing that AREN'T self-similar within the plant itself, yet still branching and perhaps representable by a totally different L-system representation from say the branching of stems and leaves (Say networks of vasculature within plants such as xylem and pholem, which we see as 'veins' within the leaves for example) - Then yeah, plants really are WAY more complex than that and they deserve a more accurate representation.

I think L-systems are beautiful and I really recommend anyone who's interested check out Lindenmayer's work on it all [1] but I think if this article has any point it's that we need more complex models to really do plants justice. I think that the fractal appearance of stuff like romanesco broccoli sure is cool but I think it's better understood as sort of a holographic projection of fractalline growth into 3d space rather than an actual 3d fractal

Like these models are super excellent for making renders of plants in 3D modelling engines but they're not REALLY plants, even if we can make them look incredibly realistic using just that basic level of modelling, some nice shaders, and some trig functions to make it look like it's blowing in the wind

[1] https://en.wikipedia.org/wiki/The_Algorithmic_Beauty_of_Plan... [1]

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

#9
There have been some HN posts on this recently. Some quick findings:

https://www.nytimes.com/2021/07/08/science/cauliflower-fract...

https://www.science.org/doi/10.1126/science.abg5999

https://ournarratives.net/cauliflowers-fractal-pattern-a-key...

Even if not a "true" fractal, for the layperson, it's close enough and does a good job of showing what is a fractal.

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

#10
post #4

Of course it's not an actual fractal, because you know, infinity... But take the Romanesco Broccoli, it really looks like a fractal. It can't be just random. There definitely is some kind of mechanism that's fractal-ish somewhere.

You can estimate Hausdorff dimensions of non-infinitessimal things, like coastlines.
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