11–20 of 71 posts
> 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…
> 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...
> 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…
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.
In other news, the golden ratio doesn’t really occur in nature as much as people would like to believe. [0]
[0] https://www.maa.org/external_archive/devlin/devlin_05_07.htm...
> 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…
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.
"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 inter…
Essentially the author is saying that fern leaf doesn’t grow as single line, and then subdivides. Well, no shit. Literally no one ever thought that. It betrays a lack of imagination where the author is conflating a single algorithm for the construction of a fractal to an actual fractal shape. It’s the same as complaining that something similar to a Sierpinski’s Triangle can’t be a fractal because it wasn’t made by placing atoms at the midpoints between it and a randomly selected exterior vertex.
Are fern leaves technically fractals? No. (And no, I am not talking about the sophomoric objection then lacking infinite regression.) Are they similar to fractals? Yes. Is it useful as an illustration of both a feactal, and how complex body plans can be encoded in DNA without actually specifying every point like a literal blueprint? Yes.
None of this is different than the discussing the similarities fractals and coastlines. No one thinks Britain is a literal fractal.
Honestly, this idea of fractals is very similar to the idea that the irrational number phi shows up it nature. When you actually look deeply at the purported examples, you’ll find out, it’s not actually there.
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.
It's also worth noting that there are other ways of "measuring" fractal dimension that do not always agree so it can be informative to also look at e.g. box counting dimension too.
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.
It isn’t random, and it also isn’t a fractal (as is explained in the very short article). In other news, the golden ratio doesn’t really occur in nature as much as people would like to believe. [0] [0] https://www.maa.org/external_archive/devlin/devlin_05_07.htm...
It’s a straw man. The fractal is an analogy; nobody seriously thinks you can zoom in or out of a cauliflower infinitely. We know about atoms and stuff. It’s just pointless pedantry.
> 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…
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.
There's this trope about physics and math envy, which I think ultimately boiled down an envy of the funding that physicists received in the cold war (it lead to a lot of equations in Ecology, for instance).
But ignoring the reasons for math envy for a moment, there's also a push among some of the more computationally inclined to try to explain other sciences using their tools. This has been going on for a least a few decades, with "holographic universe" ideas, Wolfram's "New Kind of Science", and the like, and of course actual computational modeling such as weather models. And conflating a prediction engine with intelligence (like that guy at Google did).
It's good to show that these reductions, at our current level of computational technology, are not that accurate. "Computational hacking" is really no different from "P-hacking", in that it is easily abused by the lay audience and scientists who conflate possibly fictitious correlative modeling with reality.
The model is not the thing. The P-score is not the thing. Mechanisms are the thing. Mechanisms are the core of science. All else is preliminary, at best.