Stunning Photographs of Fractals in Nature | Hacker News Reader

Stunning Photographs of Fractals in Nature

timewheel.net

33 pointsfindaway11 comments

Apart from the Romanesque cauliflower, these images mostly just show examples of phyllotactic spirals, which are not really fractals.

Fractal models can generate patterns reminiscent of some organic structures, particularly branching structures, but their importance in doing so is often overstated. Generally speaking, they don't capture the underlying biological processes giving rise to the structures; models that do (reaction-diffusion, optimal transport networks, models of specific genetic developmental programmes...) achieve more realism.

"The problem with a field such as fractal theory, which can be visually dramatic and practised without much background and sophistication, is that uninformed proselytising and inappropriate use can raise unrealistic expectations as to its relevance and applicability. ...Although chaos and fractal theory have been proposed by some as biological panaceas fortunately there are enough realists to counter this view and generally keep them in perspective." –– JD Murray, Mathematical Biology

> ... which are not really fractals.

I suspect for some people the word "fractal" just means "a pleasing shape"

These are beautiful pictures! But I'm not sure that they count as fractals. A defining feature of fractals is that they are self-similar at any scale. Most of these plants are "simply" wonderful examples of a very regular geometric structure.

Except for the broccoli. That one is arguably fractal-like. I like the broccoli.

I agree that most of these pictures are not of fractals.

I would add the lily pad, thinking cactus, cabbage and fern to the list of fractals. There are only a couple of octaves/iterations in each but there is some self similarity there.

Otherwise there are probably just a lot of Fibonacci spirals(although I haven't counted them).

For more on Fibonacci spirals see this[1] excellent video series by Vi Hart.

[1]https://www.youtube.com/watch?v=ahXIMUkSXX0

The funny part is this: That broccoli is not 'natural'. Romanesco Broccoli, like all broccoli, is a selectively-bred cultivar of Brassica oleracea. Also of that same species: kale, cabbage, cauliflower, and Brussels sprouts.

I'm not sure they count as nature either. Broccoli was cultivated from http://en.wikipedia.org/wiki/Brassica_oleracea I think

I recommend the book "The Algorithmic Beauty of Plants" by Przemyslaw Prusinkiewicz and Aristid Lindenmayer (Springer-Verlag, 1990) if you want to explore the mathematical systems behind plants like this. It covers Lindenmayer systems (L-systems) in detail, of which phyllotaxis is only a part.

I happen to have a first edition, but it is these days available as a free PDF: http://algorithmicbotany.org/papers/abop/abop.pdf

I agree with the other comments here. The images are beautiful, and "fractally" in some interesting ways, but they are not images of fractals per se.

"Fractal cabbage" is kind of awesome.

I have an extremely hard time believing what's real and what isn't anymore in terms of photography.

All of the filters...

Literally any photo you see will be 'impure'; as soon as the image is captured from the sensor, the raw data goes through many, many transformations before it arrives at the final image (white balance, exposure adjustment etc. etc.). I guess we could draw the line at how much post-processing is applied. Having said that, photography is very much an art form, and post-processing is just one of the many steps which goes into creating the intended image.

Film photography also has many variables such as film type and development process - fascinating stuff!

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